diff --git a/autofit/non_linear/plot/samples_plotters.py b/autofit/non_linear/plot/samples_plotters.py
index 2a2c1500c..98de9a919 100644
--- a/autofit/non_linear/plot/samples_plotters.py
+++ b/autofit/non_linear/plot/samples_plotters.py
@@ -35,15 +35,53 @@ def _corner_range_from(data):
     return plot_range
 
 
+def _effective_sample_size(weight_list, sample_count):
+    """Kish effective sample size ``sum(w)**2 / sum(w**2)`` of a weight list.
+
+    Row count alone does not say whether a sample can be plotted: a nested
+    sampler stopped early returns many rows of which one carries essentially all
+    the weight, so every weighted statistic ``corner`` computes (quantile
+    ``range`` most visibly) is a statistic of that single point. ``None`` or an
+    empty weight list means unweighted, for which every row counts.
+    """
+    if weight_list is None:
+        return float(sample_count)
+
+    weights = np.asarray(weight_list, dtype=float)
+
+    if weights.size == 0:
+        return float(sample_count)
+
+    sum_of_squares = np.sum(weights**2)
+
+    if sum_of_squares == 0.0:
+        return 0.0
+
+    return float(np.sum(weights) ** 2 / sum_of_squares)
+
+
 @skip_in_test_mode
 def corner_cornerpy(samples, path=None, filename="corner", format="show", **kwargs):
     data = np.asarray(samples.parameter_lists)
-    if data.ndim < 2 or data.shape[0] <= data.shape[1]:
+
+    sample_count = data.shape[0] if data.ndim >= 1 else 0
+    parameter_count = data.shape[1] if data.ndim >= 2 else 0
+    effective_sample_size = _effective_sample_size(
+        getattr(samples, "weight_list", None), sample_count
+    )
+
+    if (
+        data.ndim < 2
+        or sample_count <= parameter_count
+        or effective_sample_size <= parameter_count
+    ):
         logger.info(
-            "corner_cornerpy: skipping corner plot, only %s sample(s) for %s parameter(s) "
+            "corner_cornerpy: skipping corner plot, only %s sample(s) "
+            "(effective sample size %.2f) for %s parameter(s) "
             "(e.g. PYAUTO_TEST_MODE bypass or an early-iteration update).",
-            data.shape[0] if data.ndim >= 1 else 0,
-            data.shape[1] if data.ndim >= 2 else 0,
+            sample_count,
+            effective_sample_size,
+            parameter_count,
         )
         return
 
diff --git a/test_autofit/non_linear/plot/test_samples_plotters.py b/test_autofit/non_linear/plot/test_samples_plotters.py
index 2beec0366..3a8068a3b 100644
--- a/test_autofit/non_linear/plot/test_samples_plotters.py
+++ b/test_autofit/non_linear/plot/test_samples_plotters.py
@@ -1,3 +1,5 @@
+import logging
+
 import numpy as np
 import pytest
 
@@ -53,12 +55,12 @@ def __init__(self, labels):
 
 
 class MockSamples:
-    def __init__(self, parameter_lists, weight_list=None):
+    def __init__(self, parameter_lists, weight_list=None, labels=None):
         self.parameter_lists = parameter_lists
         self.weight_list = (
             weight_list if weight_list is not None else [1.0] * len(parameter_lists)
         )
-        self.model = MockModel(["x", "y"])
+        self.model = MockModel(labels if labels is not None else ["x", "y"])
 
 
 @pytest.fixture
@@ -177,3 +179,56 @@ def test__corner_cornerpy__degenerate_columns_still_render(monkeypatch):
     degenerate = MockSamples(parameter_lists=[[1.0, 5.0]] * 20)
 
     samples_plotters.corner_cornerpy(samples=degenerate, bins=5)
+
+
+def test__effective_sample_size__uniform_and_degenerate_weights():
+    assert samples_plotters._effective_sample_size([1.0] * 10, 10) == pytest.approx(10.0)
+
+    # One point carrying all the weight is worth a single sample, however many
+    # rows sit beside it.
+    degenerate = [0.0] * 99 + [1.0]
+    assert samples_plotters._effective_sample_size(degenerate, 100) == pytest.approx(1.0)
+
+    # No weights at all means unweighted, so every row counts.
+    assert samples_plotters._effective_sample_size(None, 7) == pytest.approx(7.0)
+    assert samples_plotters._effective_sample_size([], 7) == pytest.approx(7.0)
+
+
+def test__corner_cornerpy__weight_degenerate_sample_is_skipped_not_plotted(
+    corner_call, caplog
+):
+    # Regression (#1541): a nested sampler stopped after its first batch returns
+    # plenty of rows but one non-zero weight. `range=0.999` is then a weighted
+    # quantile over that single point, collapsing to a sliver that excludes every
+    # row, and `corner` raised "the provided 'range' is not valid or the sample
+    # is empty". The row-count guard never fired because the rows are all there.
+    rng = np.random.default_rng(0)
+    degenerate = MockSamples(
+        parameter_lists=rng.normal(size=(100, 3)).tolist(),
+        weight_list=[0.0] * 99 + [1.0],
+        labels=["x", "y", "z"],
+    )
+
+    with caplog.at_level(logging.INFO, logger=samples_plotters.__name__):
+        samples_plotters.corner_cornerpy(
+            samples=degenerate,
+            range=np.ones(3) * 0.999,
+        )
+
+    assert corner_call == {}
+    assert "skipping corner plot" in caplog.text
+    assert "effective sample size" in caplog.text
+
+
+def test__corner_cornerpy__healthy_weights_still_plot(corner_call):
+    rng = np.random.default_rng(0)
+    healthy = MockSamples(
+        parameter_lists=rng.normal(size=(100, 3)).tolist(),
+        weight_list=[1.0] * 100,
+        labels=["x", "y", "z"],
+    )
+
+    samples_plotters.corner_cornerpy(samples=healthy, range=np.ones(3) * 0.999)
+
+    assert corner_call != {}
+    assert corner_call["weights"] == healthy.weight_list