diff --git a/crates/svg/src/import/convert.rs b/crates/svg/src/import/convert.rs
index e640880e7..2a777b342 100644
--- a/crates/svg/src/import/convert.rs
+++ b/crates/svg/src/import/convert.rs
@@ -156,14 +156,16 @@ pub(super) fn drawn_ellipse(p: &usvg::tiny_skia_path::Path) -> Option<PathData>
     let (x0, x1) = ends.iter().fold((f64::INFINITY, f64::NEG_INFINITY), |(lo, hi), q| (lo.min(q.x), hi.max(q.x)));
     let (y0, y1) = ends.iter().fold((f64::INFINITY, f64::NEG_INFINITY), |(lo, hi), q| (lo.min(q.y), hi.max(q.y)));
     let (c, rx, ry) = (Point::new((x0 + x1) / 2.0, (y0 + y1) / 2.0), (x1 - x0) / 2.0, (y1 - y0) / 2.0);
-    // usvg works in f32: points match within a few of its steps at the size of the coordinates.
-    let tol = 16.0 * f64::from(f32::EPSILON) * [x0, x1, y0, y1].iter().fold(1.0f64, |m, v| m.max(v.abs()));
+    // usvg works in f32: points match within a few of its steps at the size of the coordinates, and
+    // a radius of fewer than two steps does not survive the conversion.
+    let step = f64::from(f32::EPSILON) * [x0, x1, y0, y1].iter().fold(1.0f64, |m, v| m.max(v.abs()));
+    let tol = 16.0 * step;
     let axes = [Point::new(x1, c.y), Point::new(c.x, y1), Point::new(x0, c.y), Point::new(c.x, y0)];
     let off = 1e-3 + 4.0 * tol / rx.min(ry);
     let on_ellipse = |q: &Point| (((q.x - c.x) / rx).powi(2) + ((q.y - c.y) / ry).powi(2) - 1.0).abs() <= off;
     if !closed
-        || rx <= tol
-        || ry <= tol
+        || rx < 2.0 * step
+        || ry < 2.0 * step
         || ends.first().is_none_or(|s| s.distance(axes[0]) > tol)
         || !axes.iter().all(|a| ends.iter().any(|q| q.distance(*a) <= tol))
         || !ends.iter().all(on_ellipse)
diff --git a/crates/svg/tests/it/basic_shapes.rs b/crates/svg/tests/it/basic_shapes.rs
index 8d76739b4..da759b197 100644
--- a/crates/svg/tests/it/basic_shapes.rs
+++ b/crates/svg/tests/it/basic_shapes.rs
@@ -164,9 +164,10 @@ fn circles_and_ellipses_import_as_the_ellipse_drawn() {
         <circle cx="50" cy="50" r="40" transform="translate(10 20)"/>
         <ellipse cx="100" cy="100" rx="60" ry="20" transform="rotate(30 100 100)"/>
         <ellipse cx="36.255" cy="154.118" rx="36.255" ry="5.421"/>
-        <circle cx="40000000" cy="0" r="400"/></svg>"#;
+        <circle cx="40000000" cy="0" r="400"/>
+        <ellipse cx="1000000" cy="1000000" rx="36" ry="1"/></svg>"#;
     let back = paths(&import(svg).unwrap());
-    assert_eq!(back.len(), 4);
+    assert_eq!(back.len(), 5);
     let circle = &back[0].subpaths[0].anchors;
     let want: Vec<Point> = [(100.0, 70.0), (60.0, 110.0), (20.0, 70.0), (60.0, 30.0)].map(|(x, y)| Point::new(x, y)).into();
     assert_eq!(circle.len(), 4);
@@ -182,6 +183,11 @@ fn circles_and_ellipses_import_as_the_ellipse_drawn() {
     // A small circle far from the origin too.
     let far = &back[3].subpaths[0].anchors;
     assert!(far.len() == 4 && far[0].p.distance(Point::new(40_000_400.0, 0.0)) < 8.0, "{far:?}");
+    // A radius of a few of f32's steps at its coordinates, with handles of the standard length.
+    let thin = &back[4].subpaths[0].anchors;
+    let handle = thin.first().map(|a| a.h_out - a.p);
+    assert!(thin.len() == 4 && thin[0].p.distance(Point::new(1_000_036.0, 1_000_000.0)) < 0.25, "{thin:?}");
+    assert!(handle.is_some_and(|h| h.x.abs() < 1e-6 && (h.y - shapes::KAPPA).abs() < 1e-6), "{thin:?}");
 }
 
 #[test]