diff --git a/tests/test_aggregators.py b/tests/test_aggregators.py
index b85dcd19..0b65c5ea 100644
--- a/tests/test_aggregators.py
+++ b/tests/test_aggregators.py
@@ -109,7 +109,7 @@ def test_arg_downsample_no_x_empty_series(downsampler, series):
 def test_wrap_aggregate(downsampler, gap_handler, series, index_type):
     series = series.copy()
     series.index = construct_index(series, index_type)
-    for n in np.random.randint(100, len(series), 6):
+    for n in np.random.randint(100, len(series) // 2, 6):
         # make sure n is even (required for MinMax downsampler)
         n = n - (n % 2)
         x_agg, y_agg, indices = wrap_aggregate(
@@ -234,11 +234,10 @@ def test_wrap_aggregate_range_index_data_point_selection(
 
 # ------------------------------- NAN handling -------------------------------
 @pytest.mark.parametrize("downsampler", [MinMaxLTTB, MinMaxAggregator])
-@pytest.mark.parametrize("gap_handler", [MedDiffGapHandler, NoGapHandler])
 @pytest.mark.parametrize("series", [lf("float_series")])
-def test_nan_behavior(series, downsampler, gap_handler):
+def test_nan_behavior(series, downsampler):
     series = series.copy()
-    series.iloc[np.random.choice(len(series), 100)] = np.nan
+    series.iloc[1 + np.random.choice(len(series) - 2, 100, replace=False)] = np.nan
 
     # OMIT -> no NaNs in the output
     for n in np.random.randint(100, len(series), 6):
diff --git a/tests/test_figure_resampler.py b/tests/test_figure_resampler.py
index bebd9f59..640914ec 100644
--- a/tests/test_figure_resampler.py
+++ b/tests/test_figure_resampler.py
@@ -435,7 +435,9 @@ def test_nan_retained_input(float_series):
 
     # ADD nans to to the float_series
     float_series = float_series.copy()
-    float_series.iloc[np.random.choice(len(float_series), 100, replace=False)] = np.nan
+    float_series.iloc[
+        1 + np.random.choice(len(float_series) - 2, 100, replace=False)
+    ] = np.nan
     fig.add_trace(
         go.Scatter(x=float_series.index, y=float_series, name="float_series"),
         row=1,
@@ -449,7 +451,9 @@ def test_nan_retained_input(float_series):
     assert pd.isna(fig.hf_data[0]["y"]).sum() == 100
 
     # here we test whether we are able to deal with not-nan output
-    float_series.iloc[np.random.choice(len(float_series), 100)] = np.nan
+    float_series.iloc[
+        1 + np.random.choice(len(float_series) - 2, 100, replace=False)
+    ] = np.nan
     fig.add_trace(
         go.Scatter(
             x=float_series.index, y=float_series
@@ -459,7 +463,9 @@ def test_nan_retained_input(float_series):
         col=1,
     )
 
-    float_series.iloc[np.random.choice(len(float_series), 100)] = np.nan
+    float_series.iloc[
+        1 + np.random.choice(len(float_series) - 2, 100, replace=False)
+    ] = np.nan
     fig.add_trace(
         go.Scattergl(
             x=float_series.index,
@@ -599,7 +605,7 @@ def test_hf_text_and_hf_marker_color():
 def test_hf_text_and_hf_hovertext_and_hf_marker_size_nans():
     y_orig = np.arange(10_000).astype(float)
     y = y_orig.copy()
-    y[::101] = np.nan
+    y[1::101] = np.nan
 
     # NEW from plotly-resampler >0.9.2 => we retain the NaNs in the input data and
     # the NaN handling is delegated to the aggregators
diff --git a/tests/test_figurewidget_resampler.py b/tests/test_figurewidget_resampler.py
index 90e83d51..03f73bd4 100644
--- a/tests/test_figurewidget_resampler.py
+++ b/tests/test_figurewidget_resampler.py
@@ -265,7 +265,9 @@ def test_nan_removed_input(float_series):
 
     # Add NaN's to the float series
     float_series = float_series.copy()
-    float_series.iloc[np.random.choice(len(float_series), 100, replace=False)] = np.nan
+    float_series.iloc[
+        1 + np.random.choice(len(float_series) - 2, 100, replace=False)
+    ] = np.nan
     fig.add_trace(
         go.Scatter(x=float_series.index, y=float_series, name="float_series"),
         row=1,
@@ -279,7 +281,9 @@ def test_nan_removed_input(float_series):
     assert pd.isna(fig.hf_data[0]["y"]).sum() == 100
 
     # here we test whether we are able to deal with not-nan output
-    float_series.iloc[np.random.choice(len(float_series), 100)] = np.nan
+    float_series.iloc[
+        1 + np.random.choice(len(float_series) - 2, 100, replace=False)
+    ] = np.nan
     fig.add_trace(
         go.Scatter(
             x=float_series.index, y=float_series
@@ -289,7 +293,9 @@ def test_nan_removed_input(float_series):
         col=1,
     )
 
-    float_series.iloc[np.random.choice(len(float_series), 100)] = np.nan
+    float_series.iloc[
+        1 + np.random.choice(len(float_series) - 2, 100, replace=False)
+    ] = np.nan
     fig.add_trace(
         go.Scattergl(
             x=float_series.index,