diff --git a/TODO.md b/TODO.md
index 41d14c1..cc2a818 100644
--- a/TODO.md
+++ b/TODO.md
@@ -30,6 +30,18 @@ P2: security: per-origin rate limiting
 
 # Completed Steps
 
+- 2026-10-15 a thin source requested with `fit=cover` no longer makes libvips
+  build a huge image (closes #282): libvips' thumbnail scaled the whole source
+  to cover the requested size and copied that into memory before it cut out the
+  centre, so an 8192x64 source at 8192x8192 made it allocate about 24 GiB, and
+  an 8192x1 source answered 500. The image processor now first cuts the centre
+  of the source, widened to whole source pixels, and thumbnail scales and cuts
+  only that, by the same amount on both sides as before. What it copies into
+  memory is then larger than the output by less than one scaled source pixel on
+  each side. With the runtime image's libvips and JPEG output at 8192x8192,
+  resident memory peaked at about 242 MiB for the 8192x64 source and 431 MiB for
+  the 8192x1 one. The output can sit a fraction of an output pixel from where it
+  was.
 - 2026-10-15 a `/v1/image/` URL whose source path or source query holds a `#`,
   written as `%23`, is refused with 400 (closes #286): the source URL built from
   it ended at the `#` when fetched, so each text after it fetched the same
@@ -46,16 +58,6 @@ P2: security: per-origin rate limiting
   way, and so is an IPv6 address without brackets, which needed a signature
   before. Underscores are kept because `allowlist_hosts` accepts host names
   holding them.
-- 2026-10-15 a thin source requested with `fit=cover` no longer makes libvips
-  build a huge image (closes #282): libvips scaled the whole source to cover the
-  requested size and copied that into memory before it cut out the centre, so an
-  8192x64 source at 8192x8192 made it allocate about 24 GiB, and an 8192x1
-  source answered 500. The image processor now cuts the centre of the source to
-  the requested size's proportions first and resizes that, so no image larger
-  than the source or the output is made; the crop is the same centre as before.
-  With the runtime image's libvips and JPEG output at 8192x8192, resident memory
-  peaked at about 44 MiB for the 8192x64 source, 40 MiB for the 8192x1 one, and
-  117 MiB for a 4000x3000 one, which took 373 MiB before.
 - 2026-10-15 the README says how a source URL with a query is written into an
   image URL, and the image route accepts it (closes #255): the query follows the
   source path after `%3F`. pixa now reads the image URL's path decoded once, so
diff --git a/internal/imageprocessor/imageprocessor.go b/internal/imageprocessor/imageprocessor.go
index bf08e98..716b9ad 100644
--- a/internal/imageprocessor/imageprocessor.go
+++ b/internal/imageprocessor/imageprocessor.go
@@ -530,35 +530,36 @@ func (p *ImageProcessor) resize(
 	}
 }
 
-// cropCentreAndResize cuts img to its centre, the largest area it holds with
-// the proportions of width x height, and resizes that to width x height.
-// This is the crop libvips' thumbnail makes with InterestingCentre, but
-// libvips scales the whole image to cover the size and copies the result
-// into memory before it crops, and for a thin image that is far larger than
-// the image or the output: 8192x64 at 8192x8192 is 1048576x8192, about 24
-// GiB. Cropping first makes no image larger than img or the output.
+// cropCentreAndResize scales img by the same amount on both sides, the
+// least that makes it cover width x height, and cuts the centre width x
+// height out of it, as libvips' thumbnail does with InterestingCentre.
+// thumbnail alone scales the whole image and copies the result into memory
+// before it cuts, and for a thin image that is far larger than the image or
+// the output: 8192x64 at 8192x8192 is 1048576x8192, about 24 GiB. So the
+// centre is cut from img first, widened to whole pixels of img, which adds
+// less than one pixel of img on each side, and thumbnail scales and cuts
+// only that.
 func cropCentreAndResize(img *vips.ImageRef, width, height int) error {
 	imgW, imgH := img.Width(), img.Height()
 
 	// An image wider than the requested proportions keeps its height and
-	// loses width, any other keeps its width and loses height; the side
-	// shortened is rounded to the nearest pixel and is at least 1
-	cropW, cropH := imgW, imgH
+	// loses width down to imgH*width/height, any other keeps its width and
+	// loses height down to imgW*height/width. Half of what is lost comes
+	// off each side, rounded down to whole pixels, so the part kept holds
+	// all of the centre.
+	left, top := 0, 0
 	if imgW*height > imgH*width {
-		cropW = max(1, (imgH*width+height/2)/height)
+		left = (imgW*height - imgH*width) / (2 * height) //nolint:mnd // each side
 	} else {
-		cropH = max(1, (imgW*height+width/2)/width)
+		top = (imgH*width - imgW*height) / (2 * width) //nolint:mnd // each side
 	}
 
-	// Half of what is cut comes off each side
-	left, top := (imgW-cropW)/2, (imgH-cropH)/2 //nolint:mnd // half the cut
-
-	err := img.ExtractArea(left, top, cropW, cropH)
+	err := img.ExtractArea(left, top, imgW-2*left, imgH-2*top)
 	if err != nil {
 		return err
 	}
 
-	return img.ThumbnailWithSize(width, height, vips.InterestingNone, vips.SizeForce)
+	return img.Thumbnail(width, height, vips.InterestingCentre)
 }
 
 const defaultQuality = 85