diff --git a/examples/preprocessing/movement_compensation.py b/examples/preprocessing/movement_compensation.py
index 146a8b6f290..4577a7e0a51 100644
--- a/examples/preprocessing/movement_compensation.py
+++ b/examples/preprocessing/movement_compensation.py
@@ -75,7 +75,7 @@
 
 # %%
 # Third, use raw movement compensation (restores pattern).
-raw_sss = maxwell_filter(raw, head_pos=head_pos)
+raw_sss = maxwell_filter(raw, head_pos=head_pos, mc_interp="hann")
 evoked_raw_mc = mne.Epochs(raw_sss, events, 1, -0.2, 0.8).average()
 fig = evoked_raw_mc.plot_topomap(**topo_kwargs)
 fig.suptitle("Moving: movement compensated (raw)")
diff --git a/examples/preprocessing/otp.py b/examples/preprocessing/otp.py
index 4f2d7619ab8..a7d45d4cbc7 100644
--- a/examples/preprocessing/otp.py
+++ b/examples/preprocessing/otp.py
@@ -5,8 +5,8 @@
 Plot sensor denoising using oversampled temporal projection
 ===========================================================
 
-This demonstrates denoising using the OTP algorithm :footcite:`LarsonTaulu2018`
-on data with with sensor artifacts (flux jumps) and random noise.
+This demonstrates denoising using the OTP algorithm :footcite:`LarsonTaulu2018` on data
+with with sensor artifacts (flux jumps) and random noise.
 """
 # Author: Eric Larson <larson.eric.d@gmail.com>
 #
diff --git a/mne/preprocessing/maxwell.py b/mne/preprocessing/maxwell.py
index 2e71219c127..47c5b52e0c6 100644
--- a/mne/preprocessing/maxwell.py
+++ b/mne/preprocessing/maxwell.py
@@ -1249,7 +1249,7 @@ def _check_pos(pos, coord_frame, raw, st_fixed):
                 f"first sample offset, but found {t[0]:0.4f} < {raw._first_time:0.4f}"
             )
     t = t - raw._first_time
-    if len(t) == 0 or t[0] > 0:
+    if len(t) == 0 or t[0] >= 0.5 / raw.info["sfreq"]:
         # Prepend the existing dev_head_t to make movecomp easier
         t = np.concatenate([[0.0], t])
         trans = raw.info["dev_head_t"]
@@ -1258,6 +1258,8 @@ def _check_pos(pos, coord_frame, raw, st_fixed):
             [t[[0]], rot_to_quat(trans[:3, :3]), trans[:3, 3], [0, 0, 0]]
         )
         pos = np.concatenate([dev_head_pos[np.newaxis], pos])
+    # now that we've either prepended dev_head_t or know it's zero-like, make it zero
+    t[0] = 0
     max_dist = np.sqrt(np.sum(pos[:, 4:7] ** 2, axis=1)).max()
     if max_dist > 1.0:
         warn(
diff --git a/mne/preprocessing/tests/test_maxwell.py b/mne/preprocessing/tests/test_maxwell.py
index 2f279440d1c..961dbaadcd3 100644
--- a/mne/preprocessing/tests/test_maxwell.py
+++ b/mne/preprocessing/tests/test_maxwell.py
@@ -198,7 +198,7 @@ def read_crop(fname, lims=(0, None)):
 
 @pytest.mark.slowtest
 @testing.requires_testing_data
-def test_movement_compensation(tmp_path):
+def test_movement_compensation_basic(tmp_path):
     """Test movement compensation."""
     lims = (0, 4)
     raw = read_crop(raw_fname, lims).load_data()
@@ -303,6 +303,11 @@ def test_movement_compensation(tmp_path):
     assert_meg_snr(
         raw_sss_tweak, raw_sss.copy().crop(0, 0.05), 1.4, 8.0, chpi_med_tol=5
     )
+    # smoke test a zero-like t[0]
+    head_pos_bad[0, 0] = raw._first_time + 0.1 / raw.info["sfreq"]
+    maxwell_filter(
+        raw.copy().crop(0, 0.05), head_pos=head_pos_bad, origin=mf_head_origin
+    )
 
 
 @pytest.mark.slowtest
diff --git a/tutorials/inverse/85_brainstorm_phantom_ctf.py b/tutorials/inverse/85_brainstorm_phantom_ctf.py
index 6d9db3408ee..1c0312e4f29 100644
--- a/tutorials/inverse/85_brainstorm_phantom_ctf.py
+++ b/tutorials/inverse/85_brainstorm_phantom_ctf.py
@@ -71,7 +71,7 @@
 # Maxwell filtering:
 
 raw.apply_gradient_compensation(0)  # must un-do software compensation first
-mf_kwargs = dict(origin=(0.0, 0.0, 0.0), st_duration=10.0)
+mf_kwargs = dict(origin=(0.0, 0.0, 0.0), st_duration=10.0, st_overlap=True)
 raw = mne.preprocessing.maxwell_filter(raw, **mf_kwargs)
 raw.plot()