diff --git a/autofit/mapper/prior/log_uniform.py b/autofit/mapper/prior/log_uniform.py
index 06bdcdebf..8ae4e7ed4 100644
--- a/autofit/mapper/prior/log_uniform.py
+++ b/autofit/mapper/prior/log_uniform.py
@@ -123,22 +123,18 @@ def log_prior_from_value(self, value, xp=np):
         used by ``UniformPrior.log_prior_from_value`` which drops ``-log(b - a)``
         to return ``0.0``.
 
-        Non-positive ``value`` (``value <= 0``) returns ``-inf``. Emcee's stretch
-        move proposes physical values that can leave the support and go
-        non-positive; ``-log`` of a non-positive value is ``NaN``, which propagates
-        into the summed figure-of-merit and crashes the search with
-        ``ValueError: Probability function returned NaN``. Returning ``-inf``
-        (zero density -> rejected move) keeps the figure-of-merit finite. The
-        "double where" pattern (a safe surrogate inside the ``log``) ensures no
+        Outside ``[lower_limit, upper_limit]`` the density is zero, so ``-inf`` is
+        returned — on both the NumPy and JAX paths. This bound test is the only
+        support enforcement in the search fitness path (see
+        ``UniformPrior.log_prior_from_value`` and PyAutoFit#1489): for MCMC an
+        out-of-box proposal becomes a rejected move. It also keeps the
+        figure-of-merit finite where Emcee's stretch move proposes a non-positive
+        value: ``-log`` of a non-positive value is ``NaN``, which would otherwise
+        crash the search with ``ValueError: Probability function returned NaN``.
+        The "double where" pattern (a safe surrogate inside the ``log``) ensures no
         ``log`` of a non-positive value is evaluated, avoiding NumPy
         ``RuntimeWarning``s.
 
-        The NumPy path is otherwise unnormalised and unbounded: for any positive
-        ``value`` it returns ``-log(value)`` regardless of ``[lower_limit,
-        upper_limit]`` (dropping the normalisation constant, matching
-        ``UniformPrior``'s convention of returning ``0.0``). The JAX path
-        additionally returns ``-inf`` outside ``[lower_limit, upper_limit]``.
-
         Parameters
         ----------
         value
@@ -147,10 +143,9 @@ def log_prior_from_value(self, value, xp=np):
         xp
             Array-module to dispatch on (``numpy`` or ``jax.numpy``). Default ``numpy``.
         """
-        if xp is np:
-            positive = value > 0.0
-            return xp.where(positive, -xp.log(xp.where(positive, value, 1.0)), -xp.inf)
         in_bounds = (value >= self.lower_limit) & (value <= self.upper_limit)
+        if xp is np:
+            return xp.where(in_bounds, -xp.log(xp.where(in_bounds, value, 1.0)), -xp.inf)
         return xp.where(in_bounds, -xp.log(value), -xp.inf)
 
     def log_normalisation(self, xp=np) -> float:
diff --git a/autofit/mapper/prior/uniform.py b/autofit/mapper/prior/uniform.py
index e2daa5397..4390cdf43 100644
--- a/autofit/mapper/prior/uniform.py
+++ b/autofit/mapper/prior/uniform.py
@@ -179,10 +179,20 @@ def log_prior_from_value(self, value, xp=np):
 
         This is used by certain non-linear searches (e.g. Emcee) in the log likelihood function evaluation.
 
-        For a UniformPrior this is always zero, provided the value is between the lower and upper limit.
+        For a UniformPrior this is zero inside ``[lower_limit, upper_limit]`` (the constant
+        ``-log(upper - lower)`` is dropped, see ``log_normalisation``) and ``-inf`` outside it,
+        on both the NumPy and JAX paths.
+
+        The bound test here is the only support enforcement in the search fitness path: since
+        the removal of ``assert_within_limits`` / ``PriorLimitException`` (shipped 2025.10.16.1),
+        ``instance_from_vector`` accepts out-of-support vectors without raising, so a
+        ``log_prior_from_value`` that skipped the test left the box entirely unenforced for
+        the NumPy-path searches that form a log posterior (Emcee, Zeus, Drawer, LBFGS) —
+        see PyAutoFit#1489. The ``-inf`` is what makes an out-of-box MCMC proposal a
+        rejected move.
         """
-        if xp is np:
-            return 0.0
+        if xp is np and np.ndim(value) == 0:
+            return 0.0 if self.lower_limit <= value <= self.upper_limit else -np.inf
         in_bounds = (value >= self.lower_limit) & (value <= self.upper_limit)
         return xp.where(in_bounds, xp.zeros_like(value), -xp.inf)
 
diff --git a/autofit/non_linear/clipper.py b/autofit/non_linear/clipper.py
index ceae70aae..eb11ea97b 100644
--- a/autofit/non_linear/clipper.py
+++ b/autofit/non_linear/clipper.py
@@ -22,6 +22,15 @@
 the walker simply stays put. **Rejection is the restoring mechanism the gradient
 methods lack**, and a ``Clipper`` supplies it.
 
+(Historical correction, PyAutoFit#1489: the rejection sentence above was written
+while it was FALSE on the NumPy path — between release 2025.10.16.1, which removed
+``assert_within_limits`` / ``PriorLimitException``, and the strict
+``log_prior_from_value`` bounds restored for #1489, a NumPy-path ``UniformPrior``
+returned ``0.0`` outside its box, so there was no ``-inf`` for the MCMC samplers
+to reject and walkers escaped the declared support. It was true before
+2025.10.16.1, via exception-driven resampling, and is true again now via the
+strict priors. The gradient-method reasoning below was unaffected.)
+
 Two consumers, one source of truth
 ----------------------------------
 
diff --git a/autofit/non_linear/fitness.py b/autofit/non_linear/fitness.py
index 2604d2569..e2367bef0 100644
--- a/autofit/non_linear/fitness.py
+++ b/autofit/non_linear/fitness.py
@@ -312,7 +312,13 @@ def log_likelihood_from(self, figure_of_merit, parameters):
 
         if not self.fom_is_log_likelihood:
             log_prior_list = np.array(self.model.log_prior_list_from_vector(vector=parameters, xp=np))
-            log_likelihood = log_likelihood - np.sum(log_prior_list)
+            log_prior_sum = np.sum(log_prior_list)
+            # A non-finite prior sum marks a rejected out-of-support point (the strict
+            # priors return -inf outside their bounds, PyAutoFit#1489). The figure of
+            # merit there is -inf too, and subtracting -inf from -inf is NaN — keep the
+            # -inf so history / quick-update bookkeeping stays comparable.
+            if np.isfinite(log_prior_sum):
+                log_likelihood = log_likelihood - log_prior_sum
 
         return log_likelihood
 
diff --git a/autofit/non_linear/search/mle/bfgs/search.py b/autofit/non_linear/search/mle/bfgs/search.py
index 27fdc718a..f588663b4 100644
--- a/autofit/non_linear/search/mle/bfgs/search.py
+++ b/autofit/non_linear/search/mle/bfgs/search.py
@@ -244,11 +244,12 @@ def _fit(
                 # ``minimize(bounds=None)`` is the same call as omitting it, so the
                 # default path is unchanged.
                 #
-                # Only the JAX branch is actually *exposed* to the prior-support
-                # problem: ``UniformPrior.log_prior_from_value`` returns ``0.0``
-                # unconditionally on the NumPy path, with no bound test, so there
-                # is no hard wall to fall off there. Bounds are still passed on
-                # both branches — they are correct on both, and having them
+                # Both branches are exposed to the prior-support problem:
+                # ``UniformPrior.log_prior_from_value`` returns ``-inf`` outside
+                # its bounds on the NumPy and JAX paths alike (PyAutoFit#1489
+                # restored the NumPy-side wall), so an unclipped step out of the
+                # box makes the objective non-finite on either branch. Bounds are
+                # passed on both — they are correct on both, and having them
                 # diverge by branch would be a trap of its own.
                 if analysis._use_jax:
 
diff --git a/test_autofit/mapper/prior/test_prior.py b/test_autofit/mapper/prior/test_prior.py
index 64f9702c1..1adada76b 100644
--- a/test_autofit/mapper/prior/test_prior.py
+++ b/test_autofit/mapper/prior/test_prior.py
@@ -175,6 +175,16 @@ def test__log_prior_from_value(self):
 
         assert log_prior == 0.0
 
+        # Outside the declared box the density is zero: -inf, so the searches
+        # that form a log posterior reject the sample (PyAutoFit#1489).
+        log_prior = gaussian_simple.log_prior_from_value(value=71.0)
+
+        assert log_prior == float("-inf")
+
+        log_prior = gaussian_simple.log_prior_from_value(value=-41.0)
+
+        assert log_prior == float("-inf")
+
 
 class TestLogUniformPrior:
     def test__simple_assumptions(self):
@@ -192,10 +202,12 @@ def test__non_zero_lower_limit(self):
         assert log_uniform_half.value_for(0.5) == pytest.approx(0.70710678118, 1.0e-4)
 
     def test__log_prior_from_value(self):
-        # LogUniformPrior log-density: -log(value), dropping the normalisation
-        # constant -log(log(upper / lower)). Consistent with UniformPrior's
-        # convention of returning 0.0 (dropping -log(b - a)).
-        log_uniform = af.LogUniformPrior(lower_limit=1e-8, upper_limit=1.0)
+        # LogUniformPrior log-density inside the support: -log(value), dropping
+        # the normalisation constant -log(log(upper / lower)). Consistent with
+        # UniformPrior's convention of returning 0.0 (dropping -log(b - a)).
+        # Outside [lower_limit, upper_limit] the density is zero: -inf
+        # (PyAutoFit#1489).
+        log_uniform = af.LogUniformPrior(lower_limit=1e-8, upper_limit=10.0)
 
         assert log_uniform.log_prior_from_value(value=1.0) == 0.0
         assert log_uniform.log_prior_from_value(value=2.0) == pytest.approx(
@@ -204,10 +216,11 @@ def test__log_prior_from_value(self):
         assert log_uniform.log_prior_from_value(value=4.0) == pytest.approx(
             -np.log(4.0), 1.0e-12
         )
+        assert log_uniform.log_prior_from_value(value=11.0) == float("-inf")
 
-        # The normalisation constant being dropped means the returned values
-        # do NOT depend on the (lower_limit, upper_limit) pair — only on `value`.
-        log_uniform = af.LogUniformPrior(lower_limit=50.0, upper_limit=100.0)
+        # Inside the support the dropped constant means the returned value does
+        # NOT depend on the (lower_limit, upper_limit) pair — only on `value`.
+        log_uniform = af.LogUniformPrior(lower_limit=0.5, upper_limit=100.0)
 
         assert log_uniform.log_prior_from_value(value=1.0) == 0.0
         assert log_uniform.log_prior_from_value(value=2.0) == pytest.approx(
@@ -216,6 +229,7 @@ def test__log_prior_from_value(self):
         assert log_uniform.log_prior_from_value(value=4.0) == pytest.approx(
             -np.log(4.0), 1.0e-12
         )
+        assert log_uniform.log_prior_from_value(value=0.4) == float("-inf")
 
     def test__log_prior_from_value__non_positive_returns_neg_inf(self):
         # Regression (PyAutoHeart #27 / release run 28784914443): Emcee's stretch
@@ -232,14 +246,13 @@ def test__log_prior_from_value__non_positive_returns_neg_inf(self):
             assert log_uniform.log_prior_from_value(value=-1.0) == float("-inf")
             assert log_uniform.log_prior_from_value(value=0.0) == float("-inf")
 
-        # Positive values are unchanged: the NumPy path stays unnormalised and
-        # unbounded, returning -log(value) regardless of (lower_limit, upper_limit).
+        # In-support values are unchanged, returning the unnormalised -log(value);
+        # values above upper_limit are now -inf like the rest of the excluded
+        # support (PyAutoFit#1489).
         assert log_uniform.log_prior_from_value(value=10.0) == pytest.approx(
             -np.log(10.0), 1.0e-12
         )
-        assert log_uniform.log_prior_from_value(value=1.0e4) == pytest.approx(
-            -np.log(1.0e4), 1.0e-12
-        )
+        assert log_uniform.log_prior_from_value(value=1.0e4) == float("-inf")
 
     def test__lower_limit_zero_or_below_raises_error(self):
         with pytest.raises(exc.PriorException):
diff --git a/test_autofit/mapper/prior/test_prior_bounds_1489.py b/test_autofit/mapper/prior/test_prior_bounds_1489.py
new file mode 100644
index 000000000..ee6251754
--- /dev/null
+++ b/test_autofit/mapper/prior/test_prior_bounds_1489.py
@@ -0,0 +1,199 @@
+"""
+Regression tests for PyAutoFit#1489: prior bounds must be enforced in the search
+objective on the NumPy path.
+
+Between release 2025.10.16.1 (which removed ``assert_within_limits`` /
+``PriorLimitException``) and this fix, ``UniformPrior.log_prior_from_value``
+returned ``0.0`` unconditionally on the NumPy path and ``LogUniformPrior``
+returned a finite ``-log(value)`` outside ``[lower_limit, upper_limit]``, so
+nothing in the fitness path penalised an out-of-support parameter for the
+searches that form a log posterior (Emcee, Zeus, Drawer, LBFGS). An Emcee walker
+on a poorly-constrained parameter then escaped its declared box without bound.
+
+These tests pin the restored contract: ``-inf`` outside the support on the NumPy
+path, matching the JAX path; a ``-inf`` figure of merit for an out-of-box
+vector; a NaN-free figure-of-merit inversion; and end-to-end Emcee containment.
+"""
+import warnings
+
+import numpy as np
+import pytest
+
+import autofit as af
+from autofit.non_linear.fitness import Fitness
+
+
+class TestUniformPriorBounds:
+    def test__scalar__zero_inside__neg_inf_outside(self):
+        prior = af.UniformPrior(lower_limit=-0.1, upper_limit=0.1)
+
+        assert prior.log_prior_from_value(value=0.0) == 0.0
+        assert prior.log_prior_from_value(value=0.05) == 0.0
+        assert prior.log_prior_from_value(value=0.11) == -np.inf
+        assert prior.log_prior_from_value(value=-0.11) == -np.inf
+        assert prior.log_prior_from_value(value=5.0) == -np.inf
+
+    def test__limits_are_inclusive(self):
+        prior = af.UniformPrior(lower_limit=-0.1, upper_limit=0.1)
+
+        assert prior.log_prior_from_value(value=-0.1) == 0.0
+        assert prior.log_prior_from_value(value=0.1) == 0.0
+
+    def test__array_input(self):
+        prior = af.UniformPrior(lower_limit=-0.1, upper_limit=0.1)
+
+        log_prior = prior.log_prior_from_value(value=np.array([0.0, 0.1, 0.2, -5.0]))
+
+        assert log_prior == pytest.approx(np.array([0.0, 0.0, -np.inf, -np.inf]))
+
+
+class TestLogUniformPriorBounds:
+    def test__scalar__log_density_inside__neg_inf_outside(self):
+        prior = af.LogUniformPrior(lower_limit=1e-3, upper_limit=1e3)
+
+        assert prior.log_prior_from_value(value=10.0) == pytest.approx(
+            -np.log(10.0), 1.0e-12
+        )
+        # Above the upper limit was previously a finite -log(value) — the gap
+        # that left the box unenforced from above.
+        assert prior.log_prior_from_value(value=1.0e4) == -np.inf
+        # Between zero and the lower limit was previously finite too.
+        assert prior.log_prior_from_value(value=1.0e-4) == -np.inf
+
+    def test__non_positive_returns_neg_inf_without_warning(self):
+        prior = af.LogUniformPrior(lower_limit=1e-3, upper_limit=1e3)
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", category=RuntimeWarning)
+            assert prior.log_prior_from_value(value=0.0) == -np.inf
+            assert prior.log_prior_from_value(value=-1.0) == -np.inf
+
+    def test__array_input(self):
+        prior = af.LogUniformPrior(lower_limit=1e-3, upper_limit=1e3)
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("error", category=RuntimeWarning)
+            log_prior = prior.log_prior_from_value(
+                value=np.array([10.0, 1.0e4, 1.0e-4, -1.0])
+            )
+
+        assert log_prior == pytest.approx(
+            np.array([-np.log(10.0), -np.inf, -np.inf, -np.inf])
+        )
+
+
+class GaussianWithOffset:
+    def __init__(self, centre=50.0, normalization=1.0, sigma=5.0, offset=0.0):
+        self.centre = centre
+        self.normalization = normalization
+        self.sigma = sigma
+        self.offset = offset  # ignored by the likelihood: deliberately unconstrained
+
+    def model_data_from(self, xvalues):
+        transformed = xvalues - self.centre
+        return (
+            self.normalization
+            / (self.sigma * np.sqrt(2.0 * np.pi))
+            * np.exp(-0.5 * (transformed / self.sigma) ** 2)
+        )
+
+
+class AnalysisIgnoringOffset(af.Analysis):
+    def __init__(self, data, noise_map):
+        super().__init__()
+        self.data = data
+        self.noise_map = noise_map
+        self.xvalues = np.arange(data.shape[0], dtype=float)
+
+    def log_likelihood_function(self, instance):
+        model_data = instance.model_data_from(self.xvalues)
+        residual_map = self.data - model_data
+        chi_squared = float(np.sum((residual_map / self.noise_map) ** 2.0))
+        noise_normalization = float(np.sum(np.log(2 * np.pi * self.noise_map**2.0)))
+        return -0.5 * (chi_squared + noise_normalization)
+
+
+def _make_model_and_analysis():
+    rng = np.random.default_rng(1)
+    xvalues = np.arange(100, dtype=float)
+    truth = GaussianWithOffset(centre=50.0, normalization=25.0, sigma=5.0)
+    noise = 0.1
+    data = truth.model_data_from(xvalues) + rng.normal(0.0, noise, size=xvalues.shape)
+    noise_map = np.full(xvalues.shape, noise)
+
+    model = af.Model(GaussianWithOffset)
+    model.centre = af.UniformPrior(lower_limit=0.0, upper_limit=100.0)
+    model.normalization = af.UniformPrior(lower_limit=1e-2, upper_limit=1e2)
+    model.sigma = af.UniformPrior(lower_limit=0.1, upper_limit=25.0)
+    model.offset = af.UniformPrior(lower_limit=-0.1, upper_limit=0.1)
+
+    return model, AnalysisIgnoringOffset(data=data, noise_map=noise_map)
+
+
+class TestFitnessObjective:
+    def test__out_of_box_vector__log_posterior_is_neg_inf(self):
+        model, analysis = _make_model_and_analysis()
+
+        fitness = Fitness(
+            model=model,
+            analysis=analysis,
+            paths=None,
+            fom_is_log_likelihood=False,
+        )
+
+        in_bounds = [50.0, 25.0, 5.0, 0.05]
+        out_of_box = [50.0, 25.0, 5.0, 5.0]
+
+        assert np.isfinite(fitness(parameters=in_bounds))
+        assert fitness(parameters=out_of_box) == -np.inf
+
+    def test__log_likelihood_from__out_of_box_is_not_nan(self):
+        # -inf figure of merit minus -inf log prior is NaN unless guarded; the
+        # inversion feeds history / quick-update / resume bookkeeping, which
+        # compare against it.
+        model, analysis = _make_model_and_analysis()
+
+        fitness = Fitness(
+            model=model,
+            analysis=analysis,
+            paths=None,
+            fom_is_log_likelihood=False,
+        )
+
+        out_of_box = [50.0, 25.0, 5.0, 5.0]
+        figure_of_merit = fitness(parameters=out_of_box)
+
+        log_likelihood = fitness.log_likelihood_from(
+            figure_of_merit=figure_of_merit, parameters=out_of_box
+        )
+
+        assert not np.isnan(log_likelihood)
+        assert log_likelihood == -np.inf
+
+
+class TestEmceeContainment:
+    def test__unconstrained_parameter_stays_inside_declared_box(self):
+        """
+        End-to-end: with the strict NumPy-path priors every out-of-box proposal
+        has a -inf log posterior, so Emcee rejects it and — because walkers are
+        initialised inside the box — containment is guaranteed, independent of
+        the random seed. Before the fix, the unconstrained ``offset`` escaped
+        ``UniformPrior(-0.1, 0.1)`` in 100% of accepted samples (PyAutoFit#1489).
+        """
+        model, analysis = _make_model_and_analysis()
+
+        search = af.Emcee(
+            name="test_uniform_bounds_containment_1489",
+            nwalkers=10,
+            nsteps=300,
+            iterations_per_full_update=1_000_000,
+            number_of_cores=1,
+        )
+
+        result = search.fit(model=model, analysis=analysis)
+
+        offset_samples = np.asarray(result.samples.parameter_lists)[:, 3]
+
+        assert offset_samples.size > 0
+        assert np.all(offset_samples >= -0.1)
+        assert np.all(offset_samples <= 0.1)
diff --git a/test_autofit/non_linear/test_clipper.py b/test_autofit/non_linear/test_clipper.py
index 8404fb7f3..850936036 100644
--- a/test_autofit/non_linear/test_clipper.py
+++ b/test_autofit/non_linear/test_clipper.py
@@ -368,8 +368,13 @@ def model():
 
         assert clipped_centre <= 20.0
         assert not np.isnan(clipped_centre)
-        # The unconstrained fit is free to chase the truth past the prior edge.
-        assert unbounded_centre > 20.0
+        # Since PyAutoFit#1489 the strict NumPy-path priors make the objective
+        # -inf outside the box, so even the clipper-less fit can no longer chase
+        # the truth past the prior edge — it hits an infinite wall instead of
+        # escaping. (This test previously asserted `unbounded_centre > 20.0`,
+        # pinning the pre-#1489 escape as the foil for the clipped run.)
+        assert unbounded_centre <= 20.0
+        assert not np.isnan(unbounded_centre)
 
     def test__non_bound_supporting_method_raises_rather_than_being_ignored(self):
         """