diff --git a/jwst/outlier_detection/tests/test_outlier_detection.py b/jwst/outlier_detection/tests/test_outlier_detection.py
index 4c4d3cdfb3..bca8e6361f 100644
--- a/jwst/outlier_detection/tests/test_outlier_detection.py
+++ b/jwst/outlier_detection/tests/test_outlier_detection.py
@@ -553,13 +553,13 @@ def test_outlier_step_image_weak_cr_coron(exptype, tsovisit, tmp_cwd):
 
 
 @pytest.mark.parametrize("exptype, tsovisit", exptypes_tso)
-def test_outlier_step_weak_cr_tso(exptype, tsovisit):
+@pytest.mark.parametrize("rolling_window_width", [7, 0])
+def test_outlier_step_weak_cr_tso(exptype, tsovisit, rolling_window_width):
     '''Test outlier detection with rolling median on time-varying source
-    This test fails if rolling_window_width is set to 100, i.e., take simple median
+    This test fails if rolling_window_width is set to 0, i.e., take simple median
     '''
     bkg = 1.5
     sig = 0.02
-    rolling_window_width = 7
     numsci = 50
     signal = 7.0
     im = we_many_sci(
@@ -588,8 +588,13 @@ def test_outlier_step_weak_cr_tso(exptype, tsovisit):
         assert np.all(np.isnan(result.data[i][dnu]))
         assert np.allclose(model.data[~dnu], result.data[i][~dnu])
 
-    # Verify source is not flagged
-    assert np.all(result.dq[:, 7, 7] == datamodels.dqflags.pixel["GOOD"])
+    # Verify source is not flagged for rolling median
+    if rolling_window_width == 7:
+        assert np.all(result.dq[:, 7, 7] == datamodels.dqflags.pixel["GOOD"])
+    # But this fails for simple median
+    elif rolling_window_width == 0:
+        with pytest.raises(AssertionError):
+            assert np.all(result.dq[:, 7, 7] == datamodels.dqflags.pixel["GOOD"])
 
     # Verify CR is flagged
     assert result.dq[cr_timestep, 12, 12] == OUTLIER_DO_NOT_USE
diff --git a/jwst/outlier_detection/tso.py b/jwst/outlier_detection/tso.py
index 2c0020986f..e5524bc920 100644
--- a/jwst/outlier_detection/tso.py
+++ b/jwst/outlier_detection/tso.py
@@ -4,7 +4,7 @@
 from jwst import datamodels as dm
 
 from stcal.outlier_detection.utils import compute_weight_threshold
-from .utils import flag_model_crs
+from .utils import flag_model_crs, nanmedian3D
 from ._fileio import save_median
 
 import logging
@@ -41,7 +41,7 @@ def detect_outliers(
         medians = compute_rolling_median(weighted_cube, weight_threshold, w=rolling_window_width)
 
     else:
-        medians = np.nanmedian(weighted_cube.data, axis=0)
+        medians = nanmedian3D(weighted_cube.data, overwrite_input=False)
         # this is a 2-D array, need to repeat it into the time axis
         # for consistent shape with rolling median case
         medians = np.broadcast_to(medians, weighted_cube.shape)