diff --git a/crates/epaint/src/shadow.rs b/crates/epaint/src/shadow.rs
index 71ce76c9..8b73c07e 100644
--- a/crates/epaint/src/shadow.rs
+++ b/crates/epaint/src/shadow.rs
@@ -1,3 +1,5 @@
+use emath::NumExt as _;
+
 use super::*;
 
 /// The color and fuzziness of a fuzzy shape.
@@ -16,7 +18,7 @@ pub struct Shadow {
 
     /// The width of the blur, i.e. the width of the fuzzy penumbra.
     ///
-    /// A value of 0.0 means no blur.
+    /// A value of 0.0 means a sharp shadow.
     pub blur: f32,
 
     /// Expand the shadow in all directions by this much.
@@ -47,12 +49,26 @@ impl Shadow {
             color,
         } = *self;
 
-        let rect = rect.translate(offset);
+        let rect = rect.translate(offset).expand(spread);
+
+        // We simulate a blurry shadow by tessellating a solid rectangle using a very large feathering.
+        // Feathering is usually used to make the edges of a shape softer for anti-aliasing.
+        // The tessellator can't handle blurring/feathering larger than the smallest side of the rect.
+        // Thats because the tessellator approximate very thin rectangles as line segments,
+        // and these line segments don't have rounded corners.
+        // When the feathering is small (the size of a pixel), this is usually fine,
+        // but here we have a huge feathering to simulate blur,
+        // so we need to avoid this optimization in the tessellator,
+        // which is also why we add this rather big epsilon:
+        let eps = 0.1;
+        let blur = blur.at_most(rect.size().min_elem() - eps).at_least(0.0);
+
+        // TODO(emilk): if blur <= 0, return a simple `Shape::Rect` instead of using the tessellator
 
         let rounding_expansion = spread.abs() + 0.5 * blur;
-        let rounding = rounding.into() + Rounding::from(rounding_expansion);
+        let rounding = rounding.into() + Rounding::same(rounding_expansion);
 
-        let rect = RectShape::filled(rect.expand(spread), rounding, color);
+        let rect = RectShape::filled(rect, rounding, color);
         let pixels_per_point = 1.0; // doesn't matter here
         let font_tex_size = [1; 2]; // unused since we are not tessellating text.
         let mut tessellator = Tessellator::new(