diff --git a/src/underworld3/constitutive_models.py b/src/underworld3/constitutive_models.py
index 3829776f..1c807d4a 100644
--- a/src/underworld3/constitutive_models.py
+++ b/src/underworld3/constitutive_models.py
@@ -1034,6 +1034,15 @@ def yield_anchor(self, value):
         # rebuilt, not merely revalued — and _get_yield_softness only builds it
         # alongside δ. (The power mean carries the anchor in _combine_yield itself, so
         # for that family the _reset is the whole of the update.)
+        #
+        # Discarding the softness atom ORPHANS the δ held by any
+        # YieldHomotopyControl built before this call: the control still ramps
+        # the atom it captured, and the model now reads a fresh one. That cannot
+        # bite a march, because `yield_continuation` refuses `anchor=` together
+        # with a ready-made control — so the only way to reach it is to build a
+        # control by hand, set the anchor afterwards, and read δ back off the
+        # control for diagnostics. Set the anchor BEFORE building the control
+        # (#490).
         self._yield_offset_expr = None
         self._yield_softness_expr = None
         self._reset()
@@ -1191,6 +1200,18 @@ def viscosity_min_rounding(self):
 
     @viscosity_min_rounding.setter
     def viscosity_min_rounding(self, value):
+        # A rounding scale is a width, so it is non-negative by construction:
+        # zero is the exact hard Max, positive rounds the corner. A negative
+        # value has no reading — it would sharpen the corner past Max — and
+        # since it reaches the tangent only through the compiled expression,
+        # the symptom of setting one is a solver that will not converge rather
+        # than anything naming this property (#490).
+        if value is not None and not isinstance(value, sympy.Basic):
+            if float(value) < 0.0:
+                raise ValueError(
+                    f"viscosity_min_rounding is a rounding WIDTH and cannot be "
+                    f"negative; got {value}. Use 0 for the exact Max.")
+
         self._viscosity_min_rounding = value
         self._reset()
 
diff --git a/src/underworld3/cython/petsc_generic_snes_solvers.pyx b/src/underworld3/cython/petsc_generic_snes_solvers.pyx
index dcadfe23..f3df7cf6 100644
--- a/src/underworld3/cython/petsc_generic_snes_solvers.pyx
+++ b/src/underworld3/cython/petsc_generic_snes_solvers.pyx
@@ -6783,19 +6783,36 @@ class SNES_Stokes_SaddlePt(SolverBaseClass):
         """
         pushed = self._owned_option_pushes.get(key)
         user = self._owned_option_user.get(key)
-        if self.petsc_options.hasName(key):
-            try:
-                current = type(default)(self.petsc_options.getString(key))
-            except Exception:
-                return default
-            if pushed is None or current != pushed:
-                # Never pushed by us, or the user has moved it since. Latch: from here on
-                # the option is theirs, because the next solve will read back OUR push of
-                # THEIR value and would otherwise mistake it for our own default.
-                self._owned_option_user[key] = current
-                return current
-            if user is not None:
-                return user
+        if not self.petsc_options.hasName(key):
+            # The key is gone from the options DB, so any value latched from a
+            # previous solve is gone with it. Without this the latch outlives
+            # the option: set snes_max_it=200, delete it, and the next solve
+            # correctly uses the default — but the one after that reads back
+            # OUR push of the default, finds `current == pushed`, falls through
+            # to the latched 200 and resurrects it (#490).
+            self._owned_option_user.pop(key, None)
+            return default
+
+        try:
+            current = type(default)(self.petsc_options.getString(key))
+        except Exception:
+            # The stored value will not convert to the option's type: a user who
+            # wrote `snes_max_it = "lots"`, or a key set as a bare flag and so
+            # holding None. Neither is a number this solve can use, so it takes
+            # its own default and leaves the value in the DB for PETSc to object
+            # to in its own terms (Charter: say what is swallowed and why).
+            return default
+
+        if pushed is None or current != pushed:
+            # Never pushed by us, or the user has moved it since. Latch: from here on
+            # the option is theirs, because the next solve will read back OUR push of
+            # THEIR value and would otherwise mistake it for our own default.
+            self._owned_option_user[key] = current
+            return current
+
+        if user is not None:
+            return user
+
         return default
 
     def _push_owned_option(self, key, value):
@@ -9350,13 +9367,19 @@ class SNES_Stokes_SaddlePt(SolverBaseClass):
         homotopy_options : dict, optional
             March settings passed to
             :func:`~underworld3.systems.yield_continuation.yield_continuation` —
-            ``smoother``, ``delta0``, ``down``, ``dmin``, ``entry_maxit``,
-            ``step_maxit``, ``retries``. All are defaulted; tuning them is optional.
-            ``smoother`` picks the soft-min family — ``"powermean"`` (default,
-            approaches the yield surface from below) or ``"sqrt"`` (from above). Which
-            gives the better cold entry is problem-dependent, so it is worth trying both
-            when a march will not start. Leave ``delta0`` unset unless you have a
-            reason: each family supplies its own entry, and the two δ are not the same
+            ``smoother``, ``anchor``, ``delta0``, ``down``, ``dmin``,
+            ``entry_maxit``, ``step_maxit``, ``retries``. All are defaulted; tuning
+            them is optional.
+
+            ``smoother`` picks the soft-min family — ``"powermean"`` (default) or
+            ``"sqrt"``. Which gives the better cold entry is problem-dependent, so
+            it is worth trying both when a march will not start.
+
+            Which SIDE of the exact ``Min`` the softened yield sits on belongs to
+            ``anchor``, not to the family: under the default onset anchor both
+            families sit below ``Min`` near yield. See ``yield_anchor`` on the
+            constitutive model. Leave ``delta0`` unset unless you have a reason:
+            each family supplies its own entry, and the two δ are not the same
             parameter.
 
         Returns
diff --git a/tests/test_0204_owned_option_latch.py b/tests/test_0204_owned_option_latch.py
new file mode 100644
index 00000000..9f81fe1b
--- /dev/null
+++ b/tests/test_0204_owned_option_latch.py
@@ -0,0 +1,84 @@
+"""An owned option's user latch dies with the option (#490).
+
+`solve()` re-pushes the options the solver owns, so `_resolve_owned_option` has
+to tell its own previous push from a value the user set. It does that by
+latching the user's value the first time it sees one it did not push.
+
+The latch outlived the option. Deleting the key made the next solve fall back
+correctly, but that solve pushed the default, and the one after read the default
+back, found it equal to what it had pushed, and returned the latched value
+instead. Measured on `development`:
+
+    user sets 200        -> 200
+    user deletes the key -> 50
+    next solve           -> 200      <-- resurrected, and permanent
+    and the next         -> 200
+
+The sequence is driven through `_resolve_snes_max_it` / `_push_snes_max_it`
+rather than through `solve()`: that is the pair `solve()` itself calls, and it
+takes no solve to exercise, so the test says what it means and runs in a second.
+"""
+
+import pytest
+
+import underworld3 as uw
+
+pytestmark = [pytest.mark.level_1, pytest.mark.tier_a]
+
+DEFAULT = 50
+USER = 200
+
+
+@pytest.fixture
+def solver():
+    mesh = uw.meshing.StructuredQuadBox(elementRes=(3, 3))
+    v = uw.discretisation.MeshVariable("Vlatch", mesh, mesh.dim, degree=2)
+    p = uw.discretisation.MeshVariable("Platch", mesh, 1, degree=1)
+
+    return uw.systems.Stokes(mesh, velocityField=v, pressureField=p)
+
+
+def _solve_cycle(solver):
+    """One solve's worth of the resolve-then-push pair."""
+
+    resolved = solver._resolve_snes_max_it(DEFAULT)
+    solver._push_snes_max_it(resolved)
+
+    return resolved
+
+
+def test_a_user_value_is_honoured_and_keeps_being_honoured(solver):
+    """The control: the latch does its job while the option is there."""
+
+    solver.petsc_options["snes_max_it"] = USER
+
+    assert _solve_cycle(solver) == USER
+    assert _solve_cycle(solver) == USER
+    assert _solve_cycle(solver) == USER
+
+
+def test_deleting_the_option_does_not_leave_the_value_behind(solver):
+    """Deleting the key gives the default back, and it stays given back."""
+
+    solver.petsc_options["snes_max_it"] = USER
+    assert _solve_cycle(solver) == USER
+
+    del solver.petsc_options["snes_max_it"]
+
+    assert _solve_cycle(solver) == DEFAULT
+    assert _solve_cycle(solver) == DEFAULT, (
+        "the deleted user value came back on the second solve after deletion — "
+        "the latch outlived the option it was latched from")
+    assert _solve_cycle(solver) == DEFAULT
+
+
+def test_a_second_user_value_replaces_the_first(solver):
+    """A moved value is picked up rather than shadowed by the latched one."""
+
+    solver.petsc_options["snes_max_it"] = USER
+    assert _solve_cycle(solver) == USER
+
+    solver.petsc_options["snes_max_it"] = 7
+
+    assert _solve_cycle(solver) == 7
+    assert _solve_cycle(solver) == 7
diff --git a/tests/test_1059_yield_anchor.py b/tests/test_1059_yield_anchor.py
index 16765d85..7747d12d 100644
--- a/tests/test_1059_yield_anchor.py
+++ b/tests/test_1059_yield_anchor.py
@@ -69,8 +69,12 @@ def test_delta_zero_is_exact_min_for_both_anchors():
 @pytest.mark.level_1
 @pytest.mark.tier_a
 @pytest.mark.parametrize("smoother", ("sqrt", "powermean"))
-def test_yield_anchor_keeps_onset_stress_exact(smoother):
-    """tau/tau_y = f*eta/eta_ve = 1 at f=1 for every delta. The onset anchor does NOT."""
+def test_the_yield_anchor_keeps_stress_exact_at_nominal_yield(smoother):
+    """tau/tau_y = f*eta/eta_ve = 1 at f=1 for every delta. The onset anchor does NOT.
+
+    Named for the anchor it exercises: this drives ``yield_anchor="yield"``, and
+    "onset" is the OTHER anchor — the one shown here to miss (#490).
+    """
     c = _model(smoother); c.yield_anchor = "yield"
     for d in DELTAS[smoother]:
         assert abs(eta(c, 1.0, d) - 1.0) < 1e-10, d