diff --git a/api/derive.ts b/api/derive.ts
index ecb5a4e..a257089 100644
--- a/api/derive.ts
+++ b/api/derive.ts
@@ -75,11 +75,27 @@ export const LADDER = [320, 480, 640, 960, 1280, 1920, 2560] as const;
  * Cropping in the browser is the right default when the shape is unknown. It is the wrong one when the
  * shape is known at build time, and for a carousel of square thumbnails it always is.
  *
- * ── Only at thumbnail widths ──
+ * ── The rungs are chosen against real slots and real screens ──
  *
- * These exist for grid slots. Anything larger is a picture being looked at, which is what the aspect
- * ladder and the lightbox are for — and a square crop is a loss of information that only makes sense
- * when the slot demands it.
+ * A gallery slot measures 193 CSS pixels on a phone and about 475 on a wide desktop, so the widths
+ * that matter are those times the pixel density somebody is actually holding:
+ *
+ *   193 x 1     = 193   ->  256
+ *   193 x 1.75  = 338   ->  384      (Lighthouse's emulated phone, and most Android)
+ *   193 x 3     = 579   ->  640      (a dense phone)
+ *   475 x 1     = 475   ->  480      (desktop)
+ *   475 x 2     = 950   ->  960      (retina desktop)
+ *
+ * It was 320, 480, 640, and the middle of that is the problem: a phone needing 338 could not have it,
+ * so the browser correctly took 480 and downloaded 1.4x the pixels it could use. A rung is a few
+ * kilobytes of square WebP; a missing rung is paid for on every visit by everyone whose screen falls
+ * in the gap.
+ *
+ * 960 is here for the opposite reason — the ladder stopped at 640 and a retina desktop wanting 950 had
+ * nothing, so it took 640 and showed it soft.
+ *
+ * Above this, a picture is being looked at rather than browsed, which is what the aspect ladder and the
+ * lightbox are for. A square crop is lost information and only makes sense where the slot demands it.
  *
  * ── Centre, always ──
  *
@@ -91,7 +107,7 @@ export const LADDER = [320, 480, 640, 960, 1280, 1920, 2560] as const;
  * It is a DEFAULT. A placement that sets its own crop keeps the aspect file and frames it in CSS —
  * see how the site chooses in src/media/render.ts. Nothing here knows about placements, and should not.
  */
-export const SQUARE_LADDER = [320, 480, 640] as const;
+export const SQUARE_LADDER = [256, 384, 480, 640, 960] as const;
 
 /**
  * WebP quality, by rung.