diff --git a/lib/elements/fill_stitch.py b/lib/elements/fill_stitch.py
index 77b4ac7cf..fb8838ccf 100644
--- a/lib/elements/fill_stitch.py
+++ b/lib/elements/fill_stitch.py
@@ -137,6 +137,20 @@ class FillStitch(EmbroideryElement):
     def avoid_self_crossing(self):
         return self.get_boolean_param('avoid_self_crossing', False)
 
+    @property
+    @param('smoothness_mm', _('Smoothness'),
+           tooltip=_(
+               'Smooth the stitch path.  Smoothness limits how far the smoothed stitch path ' +
+               'is allowed to deviate from the original path.  Hint: a lower stitchc tolerance may be needed too.'
+           ),
+           type='integer',
+           unit='mm',
+           default=0,
+           select_items=[('fill_method', 1)],
+           sort_index=5)
+    def smoothness(self):
+        return self.get_float_param('smoothness_mm', 0)
+
     @property
     @param('clockwise', _('Clockwise'), type='boolean', default=True, select_items=[('fill_method', 1)], sort_index=5)
     def clockwise(self):
@@ -651,9 +665,11 @@ class FillStitch(EmbroideryElement):
         if self.contour_strategy == 0:
             stitches = contour_fill.inner_to_outer(
                 tree,
+                polygon,
                 self.row_spacing,
                 self.max_stitch_length,
                 self.running_stitch_tolerance,
+                self.smoothness,
                 starting_point,
                 self.avoid_self_crossing
             )
diff --git a/lib/stitches/contour_fill.py b/lib/stitches/contour_fill.py
index 885a7e6c7..8e47518fe 100644
--- a/lib/stitches/contour_fill.py
+++ b/lib/stitches/contour_fill.py
@@ -406,11 +406,16 @@ def _find_path_inner_to_outer(tree, node, offset, starting_point, avoid_self_cro
     return LineString(result_coords)
 
 
-def inner_to_outer(tree, offset, stitch_length, tolerance, starting_point, avoid_self_crossing):
+def inner_to_outer(tree, polygon, offset, stitch_length, tolerance, smoothness, starting_point, avoid_self_crossing):
     """Fill a shape with spirals, from innermost to outermost."""
 
     stitch_path = _find_path_inner_to_outer(tree, 'root', offset, starting_point, avoid_self_crossing)
     points = [Stitch(*point) for point in stitch_path.coords]
+
+    if smoothness > 0:
+        smoothed = smooth_path(points, smoothness)
+        points = clamp_path_to_polygon(smoothed, polygon)
+
     stitches = running_stitch(points, stitch_length, tolerance)
 
     return stitches
diff --git a/lib/svg/tags.py b/lib/svg/tags.py
index 64f6c2f30..8c1dd5589 100644
--- a/lib/svg/tags.py
+++ b/lib/svg/tags.py
@@ -66,6 +66,7 @@ inkstitch_attribs = [
     'guided_fill_strategy',
     'join_style',
     'avoid_self_crossing',
+    'smoothness_mm',
     'clockwise',
     'reverse',
     'expand_mm',
diff --git a/lib/utils/geometry.py b/lib/utils/geometry.py
index c07172c70..2903bc565 100644
--- a/lib/utils/geometry.py
+++ b/lib/utils/geometry.py
@@ -182,13 +182,17 @@ def smooth_path(path, smoothness=100.0):
     coords = _remove_duplicate_coordinates(np.array(path))
     num_points = len(coords)
 
-    # splprep's s parameter seems to depend on the number of points you pass
-    # as per the docs, so let's normalize it.
-    s = round(smoothness / 100 * num_points)
+    # s is explained in this issue: https://github.com/scipy/scipy/issues/11916
+    # the smoothness parameter limits how much the smoothed path can deviate
+    # from the original path.  The standard deviation of the distance between
+    # the smoothed path and the original path is equal to the smoothness.
+    # In practical terms, if smoothness is 1mm, then the smoothed path can be
+    # up to 1mm away from the original path.
+    s = num_points * smoothness ** 2
 
     # .T transposes the array (for some reason splprep expects
     # [[x1, x2, ...], [y1, y2, ...]]
-    tck, fp, ier, msg = splprep(coords.T, s=s, nest=-1, full_output=1)
+    tck, fp, ier, msg = splprep(coords.T, s=s, k=3, nest=-1, full_output=1)
     if ier > 0:
         from ..debug import debug
         debug.log(f"error {ier} smoothing path: {msg}")