diff --git a/crates/algo/src/quantize.rs b/crates/algo/src/quantize.rs
index 4851e15293..01b44b24f5 100644
--- a/crates/algo/src/quantize.rs
+++ b/crates/algo/src/quantize.rs
@@ -247,6 +247,10 @@ fn median_cut(pts: &[([f32; 3], u32)], n: usize) -> Vec<[f32; 3]> {
 
 /// Lloyd refinement of `centers` over weighted points.
 fn kmeans(pts: &[([f32; 3], u32)], centers: &mut [[f32; 3]], iters: usize) {
+    if centers.is_empty() {
+        // No room left (the forced colours fill the palette): nothing to refine.
+        return;
+    }
     for _ in 0..iters {
         let mut sum = vec![[0.0f64; 3]; centers.len()];
         let mut cnt = vec![0.0f64; centers.len()];
@@ -690,6 +694,24 @@ mod tests {
         }
     }
 
+    #[test]
+    fn forced_colours_filling_the_count_do_not_panic() {
+        // 2 colours + Black and White (or 8 + Primaries) leaves no room for
+        // computed entries; the median cut used to return no centres and
+        // k-means indexed into the empty list.
+        let px = vec![[1.0, 1.0, 1.0, 1.0]; 16];
+        for kind in [
+            PaletteKind::Adaptive,
+            PaletteKind::Perceptual,
+            PaletteKind::Selective,
+        ] {
+            let pal = build_palette(&px, kind, 2, Forced::BlackWhite).unwrap();
+            assert_eq!(pal, vec![[0, 0, 0], [255, 255, 255]], "{kind:?}");
+            let pal = build_palette(&gradient(8, 8), kind, 8, Forced::Primaries).unwrap();
+            assert_eq!(pal.len(), 8, "{kind:?}");
+        }
+    }
+
     #[test]
     fn quantize_maps_to_palette_with_each_dither() {
         let pal = vec![[0, 0, 0], [255, 255, 255]];