diff --git a/docs/developer/subsystems/analytic-solutions.md b/docs/developer/subsystems/analytic-solutions.md
index 2fe4ae6b..9f7f079b 100644
--- a/docs/developer/subsystems/analytic-solutions.md
+++ b/docs/developer/subsystems/analytic-solutions.md
@@ -255,7 +255,7 @@ than by being exempted:
 |---|---|---|
 | `sample_points` | unit box or cube, plus faces and corners | the elliptical inclusion is not box-filling, and the conformal map is singular at its foci — a generic sampler lands on both |
 | `boundaries` | box wall labels | a curved geometry has its own |
-| `apply_boundary_conditions` | free slip or Dirichlet mixin | — |
+| `apply_boundary_conditions` | refuses, with the helpers named | every solution writes it — see below |
 | `stress_is_deviatoric` | `False` | the source publishes $\tau$ |
 
 One consequence worth knowing: `_validation.sample` returns real values, and if
@@ -265,6 +265,62 @@ real-valued without SymPy being able to prove it — but a *genuinely* complex
 result would mean the construction is wrong, and silently taking the real part
 would hide exactly that.
 
+## Boundary conditions: composed functions, not inherited wall types
+
+Every solution writes its own `apply_boundary_conditions`. It composes three
+module-level helpers, each of which takes **the boundaries it applies to**:
+
+```python
+from underworld3.analytic import free_slip, prescribed_velocity, prescribed_scalar
+
+free_slip(solver, boundaries, normal=None)          # strong rotated u.n = 0
+prescribed_velocity(solver, boundaries, velocity)   # Dirichlet velocity
+prescribed_scalar(solver, boundaries, field)        # Dirichlet scalar
+```
+
+A typical Velic solution is then three lines:
+
+```python
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+```
+
+**Why not mixins.** This started as `FreeSlipWalls` and `FixedWalls` — mixed in,
+looping over every boundary, applying one condition. That encodes "every boundary
+is a wall of the same kind", which is true of the classical box benchmarks and
+false of most of what the suite has to serve next: a spherical shell or annulus
+with different conditions on the two radii, a faulted disc, a channel driven at
+one end. A mixin cannot express those without growing a parameter for each, and
+inheritance advertises the choice as if it were part of what the solution *is*.
+Functions taking an explicit boundary list say what is imposed *where*, and a
+solution needing two kinds calls two of them:
+
+```python
+    def apply_boundary_conditions(self, solver):
+        free_slip(solver, ["Upper"])
+        prescribed_velocity(solver, ["Lower"], self.fn_velocity)
+```
+
+**The pressure nullspace is stated by the solution, not by a wall type.** It is a
+property of the domain — enclosed, so the pressure is determined only up to a
+constant — and not of any one boundary's condition. Both mixins used to set it,
+which hid that. Leaving it out on an enclosed domain is the failure this whole
+suite exists to catch: a direct solve on the singular saddle returns a quiet,
+wrong answer that only an exact solution exposes.
+
+**Curved boundaries.** `free_slip` takes an optional `normal=`. Leave it out —
+the solver's geometric facet normal is measure-weighted to match the
+straight-facet integral the assembler evaluates, and keeps the constant pressure
+a null vector to machine precision. Pass an analytic normal such as `X/|X|` only
+when the constraint must follow the *true* surface rather than the mesh; it is
+exact for the geometry but keeps a consistency error that grows with facet
+non-uniformity. `CylindricalStokes`, the one curved-geometry solution here, uses
+the default deliberately. See
+[rotated-freeslip.md](rotated-freeslip.md) ("Which normal to use").
+
 ## The stress convention is not uniform across the family
 
 **Check which stress a kernel publishes. Do not read it off the variable name.**
@@ -545,8 +601,9 @@ Starting a comparison from a smooth profile at $t > 0$ rather than from the step
 itself is the point of using these: the step is not representable on the mesh,
 which is what makes `test_1100`'s current comparison fragile.
 
-They cannot reuse the Stokes boundary-condition mixins, which apply a *velocity*.
-`_Transport` prescribes `fn_solution` on every wall instead.
+Their boundary condition prescribes the field itself, not a velocity, so it uses
+`prescribed_scalar`. `_Transport` applies `fn_solution` on every wall, and there
+is no pressure nullspace to remove.
 
 ### Transient solutions are singular at t = 0, and that changes how you use them
 
@@ -802,8 +859,8 @@ a spatial singularity (the inclusion's foci, SolCx's isoviscous limit) needs a
 integer wavenumbers; the Gardner solutions require $\psi < 0$. Ranges become
 constructor validation, which is where they stop being folklore.
 
-1. Subclass `AnalyticSolution` and one of the boundary-condition mixins
-   (`FreeSlipWalls`, `FixedWalls`) — or `_Transport` for a scalar solution.
+1. Subclass `AnalyticSolution` — or `_Transport` for a scalar solution — and
+   write `apply_boundary_conditions`, composing the helpers below.
 2. Build the exact fields on `mesh.X` in `__init__`; set `dim`, `reference`, and
    the `eqn_*` LaTeX strings that document the *problem*. Set the fields through
    `set_fields` (Stokes) or `set_scalar_field` (transport) rather than assigning
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diff --git a/src/underworld3/analytic/__init__.py b/src/underworld3/analytic/__init__.py
index f7a45858..6d7690c9 100644
--- a/src/underworld3/analytic/__init__.py
+++ b/src/underworld3/analytic/__init__.py
@@ -26,7 +26,12 @@
 underworld3.analytic._base : the contract each solution satisfies.
 """
 
-from ._base import AnalyticSolution, FreeSlipWalls, FixedWalls
+from ._base import (
+    AnalyticSolution,
+    free_slip,
+    prescribed_scalar,
+    prescribed_velocity,
+)
 
 from .inclusion import EllipticalInclusion
 from .kramer import CylindricalStokes
@@ -36,8 +41,9 @@
 
 __all__ = [
     "AnalyticSolution",
-    "FreeSlipWalls",
-    "FixedWalls",
+    "free_slip",
+    "prescribed_scalar",
+    "prescribed_velocity",
     "AdvectedFront",
     "EllipticalInclusion",
     "ErfcDiffusion",
diff --git a/src/underworld3/analytic/_base.py b/src/underworld3/analytic/_base.py
index 8bd5ee77..fbec7ec3 100644
--- a/src/underworld3/analytic/_base.py
+++ b/src/underworld3/analytic/_base.py
@@ -522,11 +522,20 @@ def set_richards_field(self, solution, conductivity, capacity):
         self.fn_capacity = sympy.sympify(capacity)
 
     def apply_boundary_conditions(self, solver):
-        """Impose the boundary conditions this solution is posed under."""
+        """Impose the boundary conditions this solution is posed under.
+
+        Every solution writes this itself, because the conditions are part of
+        the problem it answers and are not always the same on every boundary.
+        :func:`free_slip`, :func:`prescribed_velocity` and
+        :func:`prescribed_scalar` are here to be composed inside it — each takes
+        the boundaries it applies to, so a solution with a slipping wall and a
+        driven one calls both.
+        """
 
         raise NotImplementedError(
             f"{type(self).__name__} does not declare its boundary conditions. "
-            f"Mix in FreeSlipWalls or FixedWalls, or override this method."
+            f"Write apply_boundary_conditions, composing free_slip, "
+            f"prescribed_velocity or prescribed_scalar as the problem requires."
         )
 
     def _object_viewer(self):
@@ -547,39 +556,99 @@ def _object_viewer(self):
                 display(Markdown(rf"{label}: $\displaystyle {equation}$"))
 
 
-class FreeSlipWalls:
-    r"""Mixin: the solution is posed with free slip on every wall.
+# The boundary conditions solutions build from. Functions rather than mixins:
+# a mixin can only say "every boundary of this solution gets the same
+# condition", which is true of the classical box benchmarks and false of most
+# of what the suite has to serve next — a spherical shell or annulus with
+# different conditions on the two radii, a faulted disc, a channel driven at one
+# end. Composed inside a solution's own `apply_boundary_conditions`, these say
+# what is imposed WHERE, and a solution that needs two kinds calls two of them.
+#
+# The pressure nullspace is deliberately NOT set here. It is a property of the
+# domain — enclosed, so the pressure is determined only up to a constant — and
+# not of any one wall's condition, so each solution states it for itself:
+#
+#     solver.petsc_use_pressure_nullspace = True
+#
+# Leaving it out on an enclosed domain is the failure this whole suite exists to
+# catch: a direct solve on the singular saddle returns a quiet, wrong answer
+# that only an exact solution exposes.
+
+
+def free_slip(solver, boundaries, normal=None):
+    r"""Impose free slip, :math:`\mathbf u\cdot\hat{\mathbf n}=0`, on *boundaries*.
+
+    Applied as a strong *rotated* constraint (satisfied to machine precision)
+    rather than by zeroing a velocity component. On an axis-aligned box the two
+    agree; on a curved, tilted or adapted boundary only the rotated form is
+    correct, so it is the one that still holds when a solution is used to
+    validate an adapted mesh.
+
+    Parameters
+    ----------
+    solver : Stokes
+        The solver to configure.
+    boundaries : sequence of str
+        The boundary labels to constrain — not necessarily all of them.
+    normal : sympy 1 x dim Matrix, optional
+        Analytic outward normal. The default takes the solver's geometric facet
+        normal, which is consistent with the straight-facet integral the
+        assembler evaluates and is normally the right choice even on a curved
+        wall. Supply one only when the constraint must follow the TRUE surface
+        rather than the mesh; see the "Which normal to use" section of
+        ``docs/developer/subsystems/rotated-freeslip.md``.
+    """
+
+    # Passed only when the solution has actually chosen a normal, so that
+    # otherwise the solver's own geometric default governs.
+    choice = {} if normal is None else {"normal": normal}
+
+    for boundary in boundaries:
+        solver.add_rotated_freeslip_bc(0.0, boundary, **choice)
+
 
-    Free slip is imposed as a strong *rotated* constraint
-    (:math:`\mathbf u\cdot\hat{\mathbf n}=0` to machine precision) rather than by
-    zeroing a velocity component. On an axis-aligned box the two agree; on a
-    curved, tilted or adapted boundary only the rotated form is correct, so it is
-    the one that still holds when a solution is used to validate an adapted mesh.
+def prescribed_velocity(solver, boundaries, velocity):
+    """Impose a velocity on *boundaries*, component by component.
 
-    The domain is enclosed, so the pressure carries a constant nullspace and the
-    solver is told to remove it. Leaving that out is the failure this whole suite
-    exists to catch: a direct solve on the singular saddle returns a quiet, wrong
-    answer that only an exact solution exposes.
+    For a solution driven through its boundaries rather than by a body force —
+    a far-field shear, say — and for any solution whose exact velocity is not
+    tangential to the domain.
+
+    Parameters
+    ----------
+    solver : Stokes
+        The solver to configure.
+    boundaries : sequence of str
+        The boundary labels to constrain.
+    velocity : sequence of length dim
+        Usually the solution's own ``fn_velocity``, a 1 x dim sympy Matrix, but
+        any dim-long sequence will do — a solution holding a wall at rest passes
+        a tuple of zeros.
     """
 
-    def apply_boundary_conditions(self, solver):
-        for boundary in self.boundaries:
-            solver.add_rotated_freeslip_bc(0.0, boundary)
+    for boundary in boundaries:
+        solver.add_dirichlet_bc(velocity, boundary)
 
-        solver.petsc_use_pressure_nullspace = True
 
+def prescribed_scalar(solver, boundaries, field):
+    """Impose a scalar field on *boundaries*.
 
-class FixedWalls:
-    """Mixin: velocity is prescribed on every wall, from the exact solution.
+    The scalar counterpart of :func:`prescribed_velocity`, for the transport and
+    Richards families: temperature, pressure head, hydraulic head.
 
-    For solutions driven by their boundaries rather than by a body force — a
-    far-field shear, say — and for manufactured solutions whose exact velocity is
-    not tangential to the domain. The domain is again enclosed, so the pressure
-    nullspace is removed.
+    Parameters
+    ----------
+    solver : Poisson or Darcy
+        The solver to configure.
+    boundaries : sequence of str
+        The boundary labels to constrain.
+    field : sympy expression
+        Usually the solution's own ``fn_solution``. A single expression, not a
+        sequence — the bracket below is this function's job, because
+        ``add_dirichlet_bc`` takes one entry per component and a scalar solution
+        has exactly one. That is the only difference from
+        :func:`prescribed_velocity`, whose argument already is the sequence.
     """
 
-    def apply_boundary_conditions(self, solver):
-        for boundary in self.boundaries:
-            solver.add_dirichlet_bc(self.fn_velocity, boundary)
-
-        solver.petsc_use_pressure_nullspace = True
+    for boundary in boundaries:
+        solver.add_dirichlet_bc([field], boundary)
diff --git a/src/underworld3/analytic/inclusion.py b/src/underworld3/analytic/inclusion.py
index b21500a1..515de208 100644
--- a/src/underworld3/analytic/inclusion.py
+++ b/src/underworld3/analytic/inclusion.py
@@ -36,7 +36,7 @@
 
 import sympy
 
-from ._base import AnalyticSolution, FixedWalls
+from ._base import AnalyticSolution, prescribed_velocity
 
 
 def _conjugate(expression):
@@ -172,7 +172,7 @@ def _potentials(zeta, viscosity_ratio, aspect_ratio, alpha, pure_shear, simple_s
     }
 
 
-class EllipticalInclusion(FixedWalls, AnalyticSolution):
+class EllipticalInclusion(AnalyticSolution):
     r"""A viscous elliptical inclusion in a matrix under general shear.
 
     Parameters
@@ -376,6 +376,18 @@ def __init__(
         self._potentials = potentials
         self._centre = tuple(float(c) for c in centre)
 
+    def apply_boundary_conditions(self, solver):
+        """The exact velocity on every wall; the enclosed box has a pressure nullspace.
+
+        The flow is driven by the far field, so the domain boundary is where that
+        far field enters: the walls carry the exact solution rather than a slip
+        condition, and cutting the box closer to the inclusion changes only how
+        much of the analytic far field is imposed rather than solved for.
+        """
+
+        prescribed_velocity(solver, self.boundaries, self.fn_velocity)
+        solver.petsc_use_pressure_nullspace = True
+
     @property
     def semi_axes(self):
         """Long and short semi-axes of the inclusion, in physical units."""
diff --git a/src/underworld3/analytic/kramer.py b/src/underworld3/analytic/kramer.py
index 620fbe3c..13330513 100644
--- a/src/underworld3/analytic/kramer.py
+++ b/src/underworld3/analytic/kramer.py
@@ -31,7 +31,7 @@
 
 import numpy as np
 
-from ._base import AnalyticSolution
+from ._base import AnalyticSolution, free_slip, prescribed_velocity
 
 
 _INSTALL_MESSAGE = (
@@ -254,14 +254,28 @@ def error(self, field, meshvar, norm="l2"):
         return float(np.sqrt(difference / magnitude))
 
     def apply_boundary_conditions(self, solver):
-        """Free-slip or zero-slip on both walls, as the case declares."""
+        """Free-slip or zero-slip on both arcs, as the case declares.
+
+        The two boundaries are curved, and the constraint uses the solver's own
+        geometric normal rather than the analytic radial one. That is deliberate:
+        the geometric normal is the direction the straight-facet boundary
+        integral actually sees, so the constant pressure stays a null vector to
+        machine precision, where ``X/|X|`` leaves a consistency error that grows
+        with facet non-uniformity. Reach for ``normal=`` only when the constraint
+        must follow the true circle rather than the mesh — see the "Which normal
+        to use" section of ``docs/developer/subsystems/rotated-freeslip.md``.
+        """
 
         if self.boundary == "zero":
-            for wall in self.boundaries:
-                solver.add_dirichlet_bc((0.0, 0.0), wall)
+            # TODO(BUG): issue #577 — the zero-slip case leaves the pressure
+            # nullspace in place, where every other enclosed case in the suite
+            # removes it. An annulus with both arcs held at zero velocity is
+            # enclosed, so its pressure is determined only up to a constant and
+            # a direct solve on the singular saddle can return a quiet, wrong
+            # answer. Preserved here because this refactor is
+            # behaviour-preserving by contract; fix it under its own test.
+            prescribed_velocity(solver, self.boundaries, (0.0, 0.0))
             return
 
-        for wall in self.boundaries:
-            solver.add_rotated_freeslip_bc(0.0, wall)
-
+        free_slip(solver, self.boundaries)
         solver.petsc_use_pressure_nullspace = True
diff --git a/src/underworld3/analytic/richards.py b/src/underworld3/analytic/richards.py
index 2556e70f..af2cb9ab 100644
--- a/src/underworld3/analytic/richards.py
+++ b/src/underworld3/analytic/richards.py
@@ -26,7 +26,7 @@
 
 import sympy
 
-from ._base import AnalyticSolution
+from ._base import AnalyticSolution, prescribed_scalar
 
 
 def gardner_steady_saturation(y, psi_0, psi_L, L, alpha):
@@ -91,10 +91,14 @@ class _Gardner(AnalyticSolution):
     )
 
     def apply_boundary_conditions(self, solver):
-        """Prescribe the exact head on every wall."""
+        """Prescribe the exact head on every wall.
 
-        for boundary in self.boundaries:
-            solver.add_dirichlet_bc([self.fn_solution], boundary)
+        Both Gardner solutions are column problems posed with their own head on
+        the boundary. A member needing a flux condition on the base instead
+        writes its own method and composes the helpers per boundary.
+        """
+
+        prescribed_scalar(solver, self.boundaries, self.fn_solution)
 
     def _gardner_material(self, head):
         r"""Conductivity and capacity for a given head expression.
diff --git a/src/underworld3/analytic/transport.py b/src/underworld3/analytic/transport.py
index ce2c0054..15304440 100644
--- a/src/underworld3/analytic/transport.py
+++ b/src/underworld3/analytic/transport.py
@@ -16,25 +16,29 @@
 
 import sympy
 
-from ._base import AnalyticSolution
+from ._base import AnalyticSolution, prescribed_scalar
 
 
 class _Transport(AnalyticSolution):
     """Shared metadata and boundary conditions for the scalar solutions.
 
-    These prescribe the field itself on the boundary, so they cannot reuse the
-    Stokes mixins — `FixedWalls` applies a velocity, which a scalar solution does
-    not have.
+    The whole family is posed with its own exact field on every wall, which is
+    why the condition is stated once here. A member that needs something else on
+    one boundary — a no-flux base, an inflow face — writes its own
+    ``apply_boundary_conditions`` and composes the helpers per boundary.
     """
 
     solves = "transport"
     dim = 2
 
     def apply_boundary_conditions(self, solver):
-        """Prescribe the exact field on every wall."""
+        """Prescribe the exact field on every wall.
 
-        for boundary in self.boundaries:
-            solver.add_dirichlet_bc([self.fn_solution], boundary)
+        There is no pressure nullspace to remove: the field is pinned by its own
+        Dirichlet data everywhere on the boundary.
+        """
+
+        prescribed_scalar(solver, self.boundaries, self.fn_solution)
 
 
 class Poisson1D(_Transport):
diff --git a/src/underworld3/analytic/velic.py b/src/underworld3/analytic/velic.py
index c97205e1..cc0e9ec3 100644
--- a/src/underworld3/analytic/velic.py
+++ b/src/underworld3/analytic/velic.py
@@ -17,7 +17,7 @@
 
 import sympy
 
-from ._base import AnalyticSolution, FixedWalls, FreeSlipWalls
+from ._base import AnalyticSolution, free_slip, prescribed_velocity
 from ._transcribe import (
     CSource,
     evaluate_block,
@@ -113,7 +113,7 @@ def _solcx_kernel(variant="_solCx_A"):
     }
 
 
-class SolCx(FreeSlipWalls, AnalyticSolution):
+class SolCx(AnalyticSolution):
     r"""Isoviscous-column Stokes flow with a viscosity step — the SolCx benchmark.
 
     Viscosity jumps from :math:`\eta_A` to :math:`\eta_B` at :math:`x = x_c` on
@@ -234,6 +234,12 @@ def __init__(self, mesh, eta_A=1.0, eta_B=1.0e6, x_c=0.5, n=1, reference=False):
         if reference:
             self._use_reference_kernel()
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
     def velocity_error(self, velocity_var):
         """Global relative L2 velocity error. Equivalent to ``error("velocity", ...)``."""
 
@@ -344,7 +350,7 @@ def block(name, signature):
     }
 
 
-class SolNL(FixedWalls, AnalyticSolution):
+class SolNL(AnalyticSolution):
     r"""Power-law viscous flow — the SolNL nonlinear benchmark.
 
     A manufactured solution for a shear-thinning fluid: the viscosity depends on
@@ -447,6 +453,12 @@ def __init__(self, mesh, eta_0=1.0, n=1, r=1.5, reference=False):
         if reference:
             self._use_reference_kernel()
 
+    def apply_boundary_conditions(self, solver):
+        """The exact velocity on all four walls — SolNL is driven by its boundaries."""
+
+        prescribed_velocity(solver, self.boundaries, self.fn_velocity)
+        solver.petsc_use_pressure_nullspace = True
+
     def _use_reference_kernel(self):
         """Point-evaluation only: opaque to the JIT, so no solver can use it."""
 
@@ -523,7 +535,7 @@ def _solkx_kernel():
     }
 
 
-class SolKx(FreeSlipWalls, AnalyticSolution):
+class SolKx(AnalyticSolution):
     r"""Stokes flow with an exponentially varying viscosity — the SolKx benchmark.
 
     Viscosity :math:`\eta = e^{2Bx}` on the unit box, driven by the density
@@ -624,6 +636,12 @@ def __init__(self, mesh, B=2.302585092994046, n=3, m=2):
             ),
         )
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
 
 _Y = sympy.Symbol("y")
 _BETA = sympy.Symbol("Beta")
@@ -677,11 +695,21 @@ def block(method):
     return fields
 
 
-class _SolDB(FixedWalls, AnalyticSolution):
+class _SolDB(AnalyticSolution):
     """Shared assembly for the Dohrmann–Bochev manufactured solutions."""
 
     stress_is_deviatoric = True
 
+    def apply_boundary_conditions(self, solver):
+        """The exact velocity on every wall; the enclosed box has a pressure nullspace.
+
+        These are manufactured solutions whose velocity is not tangential to the
+        box, so free slip would be a different problem.
+        """
+
+        prescribed_velocity(solver, self.boundaries, self.fn_velocity)
+        solver.petsc_use_pressure_nullspace = True
+
     def _assemble(self, mesh, values, names):
         kernel = {
             field: expression.subs(values)
@@ -826,7 +854,7 @@ def _solkz_kernel():
     }
 
 
-class SolKz(FreeSlipWalls, AnalyticSolution):
+class SolKz(AnalyticSolution):
     r"""Stokes flow with a depth-dependent viscosity — the SolKz benchmark.
 
     Viscosity :math:`\eta = e^{2Bz}` on the unit box, free slip everywhere,
@@ -909,6 +937,12 @@ def __init__(self, mesh, B=2.302585092994046, n=3, m=2):
             ),
         )
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
 
 _SIGMA = sympy.Symbol("sigma")
 
@@ -950,7 +984,7 @@ def _solab_kernel(name):
     }
 
 
-class _SolAB(FreeSlipWalls, AnalyticSolution):
+class _SolAB(AnalyticSolution):
     """Shared assembly for the two isoviscous Velic solutions."""
 
     dim = 2
@@ -1032,6 +1066,12 @@ def __init__(self, mesh, sigma=1.0, eta=1.0, n=3, m=2):
             ),
         )
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
 
 class SolA(_SolAB):
     r"""Isoviscous Stokes flow with a sinusoidal body force — the SolA benchmark.
@@ -1157,7 +1197,7 @@ def block(method):
     }
 
 
-class SolM(FreeSlipWalls, AnalyticSolution):
+class SolM(AnalyticSolution):
     r"""Stokes flow with a laterally oscillating viscosity — the SolM benchmark.
 
     Viscosity :math:`\eta = 1 + \eta_0(1 + \cos(r\pi x))` on the unit box, free
@@ -1250,6 +1290,12 @@ def __init__(self, mesh, eta_0=1.0, n=3, m=2, r=4.0):
             ),
         )
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
 
 _XC_C = sympy.Symbol("xc_solc")
 
@@ -1321,7 +1367,7 @@ def _solc_kernel(modes):
     return totals
 
 
-class SolC(FreeSlipWalls, AnalyticSolution):
+class SolC(AnalyticSolution):
     r"""Isoviscous flow driven by a dense column — the SolC benchmark.
 
     Constant viscosity on the unit box, free slip everywhere, driven by a density
@@ -1410,6 +1456,12 @@ def __init__(self, mesh, sigma=1.0, eta=1.0, x_c=0.5, modes=40):
             ),
         )
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
 
 _ZC, _DX, _X0 = sympy.symbols("zc dx x0")
 
@@ -1508,7 +1560,7 @@ def across(symbol):
     return totals
 
 
-class SolDA(FreeSlipWalls, AnalyticSolution):
+class SolDA(AnalyticSolution):
     r"""A dense column in a layered fluid — the SolDA benchmark.
 
     A rectangular density anomaly of width *dx* centred at *x_0*, in a fluid
@@ -1620,6 +1672,12 @@ def __init__(
             ),
         )
 
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all four walls; the enclosed box has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
+
 
 _DY = sympy.Symbol("dy")
 
@@ -1695,7 +1753,7 @@ def _solh_kernel(modes):
     return totals
 
 
-class SolH(FreeSlipWalls, AnalyticSolution):
+class SolH(AnalyticSolution):
     r"""A dense block in three dimensions — the SolH benchmark.
 
     Isoviscous flow in the unit cube, free slip everywhere, driven by a
@@ -1783,3 +1841,9 @@ def __init__(self, mesh, sigma=1.0, eta=1.0, dx=0.5, dy=0.5, modes=6):
                 (kernel["stress_xz"], kernel["stress_yz"], kernel["stress_zz"]),
             ),
         )
+
+    def apply_boundary_conditions(self, solver):
+        """Free slip on all six faces; the enclosed cube has a pressure nullspace."""
+
+        free_slip(solver, self.boundaries)
+        solver.petsc_use_pressure_nullspace = True
diff --git a/tests/test_1016_analytic_contract.py b/tests/test_1016_analytic_contract.py
index 6b714c0b..7ebdac4d 100644
--- a/tests/test_1016_analytic_contract.py
+++ b/tests/test_1016_analytic_contract.py
@@ -2,9 +2,9 @@
 
 `uw.analytic` is the namespace for exact solutions used to validate a solve.
 These tests fix the contract itself — that the base class exposes the fields and
-error norms every solution promises, that the boundary-condition mixins configure
-a solver rather than returning something the caller has to apply, and that a
-solution reached through the new namespace is the *same object* as the one
+error norms every solution promises, that the boundary-condition helpers
+configure a solver rather than returning something the caller has to apply, and
+that a solution reached through the new namespace is the *same object* as the one
 reached through the old one.
 
 That last check matters more than it looks: `uw.function.analytic` is a compiled
@@ -31,7 +31,7 @@ def mesh():
     )
 
 
-class Quadratic(uw.analytic.FixedWalls, uw.analytic.AnalyticSolution):
+class Quadratic(uw.analytic.AnalyticSolution):
     r"""A manufactured Stokes solution used to exercise the contract.
 
     Divergence-free by construction: :math:`\mathbf u = (y, -x)` is a rigid
@@ -56,10 +56,23 @@ def __init__(self, mesh):
         self.fn_strainrate = sympy.Matrix([[0, 0], [0, 0]])
         self.fn_stress = sympy.Matrix([[0, 0], [0, 0]])
 
+    def apply_boundary_conditions(self, solver):
+        uw.analytic.prescribed_velocity(solver, self.boundaries, self.fn_velocity)
+        solver.petsc_use_pressure_nullspace = True
+
 
 def test_contract_is_exported():
-    """The contract and the mixins are reachable from the package namespace."""
-    for name in ("AnalyticSolution", "FreeSlipWalls", "FixedWalls"):
+    """The contract and the BC helpers are reachable from the package namespace.
+
+    A solution written outside this package has to be able to reach the helpers
+    it composes, so they are public API rather than a private convenience.
+    """
+    for name in (
+        "AnalyticSolution",
+        "free_slip",
+        "prescribed_scalar",
+        "prescribed_velocity",
+    ):
         assert name in uw.analytic.__all__
         assert hasattr(uw.analytic, name)
 
@@ -266,8 +279,8 @@ class NoBoundaryConditions(uw.analytic.AnalyticSolution):
         sol.apply_boundary_conditions(stokes)
 
 
-def test_fixed_walls_configures_the_solver(mesh):
-    """FixedWalls imposes the exact velocity on every wall and kills the nullspace."""
+def test_prescribed_velocity_configures_the_solver(mesh):
+    """The velocity helper imposes the exact velocity on the boundaries it is given."""
     sol = Quadratic(mesh)
     stokes = uw.systems.Stokes(mesh)
 
@@ -277,8 +290,8 @@ def test_fixed_walls_configures_the_solver(mesh):
     assert {bc.boundary for bc in stokes.essential_bcs} == set(sol.boundaries)
 
 
-def test_free_slip_walls_uses_the_rotated_constraint(mesh):
-    """FreeSlipWalls imposes u.n = 0 by rotation, not by masking a component.
+def test_free_slip_uses_the_rotated_constraint(mesh):
+    """free_slip imposes u.n = 0 by rotation, not by masking a component.
 
     Component masking is only equivalent on an axis-aligned box; the rotated form
     is what still holds when a solution is used to validate a curved or adapted
@@ -286,20 +299,76 @@ def test_free_slip_walls_uses_the_rotated_constraint(mesh):
     is the only signal that distinguishes the two paths.
     """
 
-    class FreeSlip(uw.analytic.FreeSlipWalls, Quadratic):
-        pass
-
-    sol = FreeSlip(mesh)
+    sol = Quadratic(mesh)
     stokes = uw.systems.Stokes(mesh)
 
-    sol.apply_boundary_conditions(stokes)
+    uw.analytic.free_slip(stokes, sol.boundaries)
 
-    assert stokes.petsc_use_pressure_nullspace
     registered = {boundary for boundary, _ in stokes._rotated_freeslip_bcs}
     assert registered == set(sol.boundaries)
     assert stokes.essential_bcs == []
 
 
+def test_boundaries_can_carry_different_conditions(mesh):
+    """The reason the helpers take a boundary list rather than reading self.
+
+    A shell, an annulus or a channel is not "walls of one kind": the condition
+    differs from one boundary to the next. A solution says so by calling more
+    than one helper, each with the boundaries it applies to.
+    """
+
+    sol = Quadratic(mesh)
+    stokes = uw.systems.Stokes(mesh)
+
+    uw.analytic.free_slip(stokes, ["Left", "Right"])
+    uw.analytic.prescribed_velocity(stokes, ["Bottom", "Top"], sol.fn_velocity)
+
+    slipping = {boundary for boundary, _ in stokes._rotated_freeslip_bcs}
+    driven = {bc.boundary for bc in stokes.essential_bcs}
+
+    assert slipping == {"Left", "Right"}
+    assert driven == {"Bottom", "Top"}
+
+
+def test_free_slip_passes_an_analytic_normal_through(mesh):
+    """A curved-boundary solution can choose the normal; otherwise it says nothing.
+
+    The distinction is between passing `normal=None` and not passing `normal` at
+    all: the first overrides the solver's default with nothing, the second leaves
+    the solver to choose. So this records the *call*, rather than reading the
+    value back off the solver — reading it back would only confirm what the
+    solver's own default happens to be.
+    """
+
+    x, y = mesh.X
+    radial = sympy.Matrix([[x, y]]) / sympy.sqrt(x**2 + y**2)
+
+    class Recorder:
+        def __init__(self):
+            self.calls = []
+
+        def add_rotated_freeslip_bc(self, value, boundary, **kwargs):
+            self.calls.append((value, boundary, kwargs))
+
+    solver = Recorder()
+    uw.analytic.free_slip(solver, ["Left"])
+    uw.analytic.free_slip(solver, ["Right"], normal=radial)
+
+    assert solver.calls == [
+        (0.0, "Left", {}),
+        (0.0, "Right", {"normal": radial}),
+    ]
+
+
+def test_free_slip_reaches_a_real_solver(mesh):
+    """The recorded call is the one a Stokes solver actually accepts."""
+
+    stokes = uw.systems.Stokes(mesh)
+    uw.analytic.free_slip(stokes, ["Left"])
+
+    assert {boundary for boundary, _ in stokes._rotated_freeslip_bcs} == {"Left"}
+
+
 def test_boundaries_follow_the_mesh_dimension(mesh):
     sol = Quadratic(mesh)
     assert sol.boundaries == ["Left", "Right", "Bottom", "Top"]
diff --git a/tests/test_1024_analytic_conformance.py b/tests/test_1024_analytic_conformance.py
index 209be181..a323ef03 100644
--- a/tests/test_1024_analytic_conformance.py
+++ b/tests/test_1024_analytic_conformance.py
@@ -270,7 +270,7 @@ def test_stress_and_strain_rate_agree(name, built):
             assert np.abs(_validation.sample(sol, difference, points)).max() / scale < 1.0e-8
 
 
-# The boundary-condition mixins are exercised in test_1016_analytic_contract.py.
+# The boundary-condition helpers are exercised in test_1016_analytic_contract.py.
 # Building a Stokes solver per solution here as well was not worth what it cost:
 # it dominated the runtime of this file without checking anything the contract
 # tests do not already cover.