diff --git a/crates/trace/src/quantize.rs b/crates/trace/src/quantize.rs
index 4a0225ac2..ce51bf72d 100644
--- a/crates/trace/src/quantize.rs
+++ b/crates/trace/src/quantize.rs
@@ -1271,21 +1271,7 @@ fn rare_colours(img: &Raster, own: &[bool], choose: &[bool], hk: &HistKey, cente
             *o = best.and_then(|b| b.2);
         }
     }
-    let mut out: Vec<[f64; 3]> = vec![];
-    let mut traced_as = vec![];
-    for (((_, _, c, _), o), &from) in chosen.iter().zip(&onto).zip(&other_of) {
-        if let Some(o) = o {
-            traced_as.push((*c, *o, from));
-            continue;
-        }
-        if out.len() >= RARE_BUDGET {
-            break;
-        }
-        let lab = oklab(*c);
-        if out.iter().all(|o| dist(oklab(*o), lab) >= RARE_APART) {
-            out.push(*c);
-        }
-    }
+    let (out, traced_as) = kept_rare(chosen.iter().zip(&onto).zip(&other_of).map(|(((_, _, c, _), o), &from)| (*c, *o, from)));
     // The index in `centers` followed by `out` of a palette color or a rare color, or of the kept
     // rare color one that is not kept traces as.
     let index = |from: usize| -> Option<usize> {
@@ -1309,6 +1295,33 @@ fn rare_colours(img: &Raster, own: &[bool], choose: &[bool], hk: &HistKey, cente
     (out, traced_as)
 }
 
+/// Of `colors` (a rare color, the rare color it traces as, and where the other color of its pair
+/// comes from), largest region first: the rare colors kept, at most [`RARE_BUDGET`] and each at
+/// least [`RARE_APART`] from the ones before it, and every color that traces as another, past the
+/// budget too.
+pub(crate) fn kept_rare(colors: impl IntoIterator<Item = ([f64; 3], Option<[f64; 3]>, Option<usize>)>) -> (Vec<[f64; 3]>, Vec<TracedAsColor>) {
+    let dist = |a: [f64; 3], b: [f64; 3]| (0..3).map(|k| (a[k] - b[k]).powi(2)).sum::<f64>().sqrt();
+    let mut out: Vec<[f64; 3]> = vec![];
+    let mut traced_as = vec![];
+    for (c, o, from) in colors {
+        if let Some(o) = o {
+            traced_as.push((c, o, from));
+            continue;
+        }
+        if out.len() >= RARE_BUDGET {
+            continue;
+        }
+        let lab = oklab(c);
+        if out.iter().all(|o| dist(oklab(*o), lab) >= RARE_APART) {
+            out.push(c);
+        }
+    }
+    (out, traced_as)
+}
+
+/// A color, the rare color it traces as, and where the other color of its pair comes from.
+pub(crate) type TracedAsColor = ([f64; 3], [f64; 3], Option<usize>);
+
 /// Whether `c` (sRGB) lies between two of `centers`, as anti-aliasing mixes them: within 12 levels
 /// of the line between them, and at least an eighth of the way from each.
 fn is_mix(c: [f64; 3], centers: &[[f64; 3]]) -> bool {
diff --git a/crates/trace/src/tests.rs b/crates/trace/src/tests.rs
index 74bf738a1..6ad909495 100644
--- a/crates/trace/src/tests.rs
+++ b/crates/trace/src/tests.rs
@@ -2461,13 +2461,24 @@ fn automatic_traces_an_outline_over_a_cut_edge_in_the_color_of_other_art() {
             .iter()
             .any(|&(x0, y0, x1, y1)| (x0..x1).contains(&x) && (y0..y1).contains(&y))
     };
+    // The dark paths reach the top and the bottom of the disc, which no bar comes near: the outline
+    // is traced, not only the bars.
+    use kurbo::Shape;
+    let target = quantize::tests_oklab([110, 80, 40]);
+    let dark_reaches = |res: &TraceResult, edge: &dyn Fn(kurbo::Rect) -> bool| {
+        res.paths.iter().any(|p| {
+            let o = quantize::tests_oklab(p.color);
+            (0..3).map(|k| (o[k] - target[k]).powi(2)).sum::<f64>().sqrt() <= 3.0 && edge(p.path.to_bezpath().bounding_box())
+        })
+    };
     let mut failed = vec![];
     for width in [1.5, 2.0, 2.5] {
         let outline = move |x: f64, y: f64| (r(x, y) - 140.0).abs() < width / 2.0;
         let img = cut_out_layers(&[(&disc, light, 1.0), (&block, blue, 1.0), (&bars, dark, 1.0), (&outline, dark, 0.8)]);
         for detail in [85.0, 50.0] {
             let res = trace(&img, &TraceParams { color_detail: detail, ..preset("Auto Color").unwrap() });
-            if distinct_colours(&res) != 3 || !has_colour(&res, [110, 80, 40], 3.0) || res.paths.len() > 24 {
+            let ring = dark_reaches(&res, &|b| b.y0 < 15.0) && dark_reaches(&res, &|b| b.y1 > 285.0);
+            if distinct_colours(&res) != 3 || !has_colour(&res, [110, 80, 40], 3.0) || !ring || res.paths.len() > 24 {
                 failed.push(format!("outline {width} px, color detail {detail}: {} paths, {:?}", res.paths.len(), res.palette));
             }
         }
@@ -2546,6 +2557,26 @@ fn automatic_keeps_an_opaque_line_between_two_kept_colors() {
     assert!(has_colour(&res, [204, 190, 155], 3.0), "{:?}", res.palette);
 }
 
+#[test]
+fn a_cut_edge_blend_past_the_rare_budget_still_traces_as_its_kept_color() {
+    // Seven distinct rare colors, largest first, fill the budget of six, and then the blend of the
+    // first one along a cut edge: the blend still traces as that kept color.
+    let rare: [[f64; 3]; 7] = [
+        [200.0, 30.0, 40.0],
+        [30.0, 160.0, 60.0],
+        [240.0, 200.0, 20.0],
+        [120.0, 40.0, 160.0],
+        [20.0, 200.0, 210.0],
+        [250.0, 120.0, 180.0],
+        [90.0, 60.0, 20.0],
+    ];
+    let blend = [220.0, 120.0, 120.0];
+    let colors = rare.iter().map(|&c| (c, None, None)).chain([(blend, Some(rare[0]), None)]);
+    let (out, traced_as) = quantize::kept_rare(colors);
+    assert_eq!(out, rare[..6]);
+    assert_eq!(traced_as, [(blend, rare[0], None)]);
+}
+
 #[test]
 fn noise_keeps_a_kept_rare_colours_regions_but_not_its_specks() {
     // Labels: 0 background, 1 a rare colour kept on purpose (four islands of 4, 6, 9 and 2