diff --git a/TODO.md b/TODO.md
index 50dd5ba..870f934 100644
--- a/TODO.md
+++ b/TODO.md
@@ -26,10 +26,7 @@ resolved. The disk cache is now size-bounded with LRU eviction
 
 # Next Step
 
-P1: security: a size with one side `0` whose side computed from the source's
-proportions rounds down to 0 comes out square, can make libvips ask for about 39
-GB (an 8192x1 source at `1300x0`), or answers 500
-(https://git.eeqj.de/sneak/pixa/issues/283)
+P2: security: per-origin rate limiting
 
 # Completed Steps
 
@@ -46,6 +43,17 @@ GB (an 8192x1 source at `1300x0`), or answers 500
   another way, such as with `%2F` in the path, whatever else the path holds, or
   with a user name and password. It also answers 400 for a source path holding a
   `..` segment, as `/v1/image/` refuses one.
+- 2026-10-16 a size with one side `0` keeps the side computed from the source's
+  proportions at 1 or more (closes #283): it was rounded down, so for a thin
+  source it came out at 0, and libvips then made the size square. An 8192x1
+  source at `100x0` came out at 100x100, and at `1300x0` with `fit=cover` made
+  libvips ask for about 39 GB at once; an 8192x2 source at `100x0` answered 500.
+  `fit=contain` and `fit=inside` work both sides out again from the smaller of
+  the two scales, and keep each at 1 or more too, so a 1x8192 source at `0x100`
+  no longer answers 500 there. An 8192x1 source at `1300x0` now comes out at
+  1300x1, and the process running it alone peaked at about 34 MiB resident. With
+  `fit=outside` the image is scaled to cover the size, so that source at `100x0`
+  comes out at 8192x1.
 - 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
@@ -1013,7 +1021,6 @@ GB (an 8192x1 source at `1300x0`), or answers 500
 
 # Future Steps
 
-- P2: security: per-origin rate limiting
 - P2: HTTP response handling
     - Last-Modified headers
 - P2: configuration
diff --git a/internal/imageprocessor/imageprocessor.go b/internal/imageprocessor/imageprocessor.go
index 716b9ad..0c315ea 100644
--- a/internal/imageprocessor/imageprocessor.go
+++ b/internal/imageprocessor/imageprocessor.go
@@ -311,8 +311,10 @@ func (p *ImageProcessor) Process(
 
 // targetDimensions calculates the output dimensions for a requested size,
 // scaling proportionally when only one dimension is given and keeping the
-// original dimensions when both are zero. A side scaled proportionally can
-// come out above MaxOutputDimension, which is ErrOutputTooLarge.
+// original dimensions when both are zero. A side scaled proportionally is
+// rounded down but kept at 1 or more, as for a thin image it would round
+// down to 0, a side of no pixels. It can come out above MaxOutputDimension,
+// which is ErrOutputTooLarge.
 func targetDimensions(size Size, origWidth, origHeight int) (int, int, error) {
 	width, height := size.Width, size.Height
 
@@ -322,10 +324,10 @@ func targetDimensions(size Size, origWidth, origHeight int) (int, int, error) {
 		return origWidth, origHeight, nil
 	case width == 0:
 		// Only height specified: calculate width proportionally
-		width = origWidth * height / origHeight
+		width = max(1, origWidth*height/origHeight)
 	case height == 0:
 		// Only width specified: calculate height proportionally
-		height = origHeight * width / origWidth
+		height = max(1, origHeight*width/origWidth)
 	}
 
 	if width > MaxOutputDimension || height > MaxOutputDimension {
@@ -479,13 +481,16 @@ func (p *ImageProcessor) resize(
 		return cropCentreAndResize(img, width, height)
 
 	case FitContain:
-		// Resize to fit within dimensions, maintaining aspect ratio
+		// Resize to fit within dimensions, maintaining aspect ratio. Scaled
+		// by the smaller scale, the short side of a thin image can round
+		// down to 0, which libvips refuses as a width, so each side is at
+		// least 1.
 		imgW, imgH := img.Width(), img.Height()
 		scaleW := float64(width) / float64(imgW)
 		scaleH := float64(height) / float64(imgH)
 		scale := min(scaleW, scaleH)
-		newW := int(float64(imgW) * scale)
-		newH := int(float64(imgH) * scale)
+		newW := max(1, int(float64(imgW)*scale))
+		newH := max(1, int(float64(imgH)*scale))
 
 		return img.Thumbnail(newW, newH, vips.InterestingNone)
 
@@ -503,8 +508,8 @@ func (p *ImageProcessor) resize(
 		scaleW := float64(width) / float64(imgW)
 		scaleH := float64(height) / float64(imgH)
 		scale := min(scaleW, scaleH)
-		newW := int(float64(imgW) * scale)
-		newH := int(float64(imgH) * scale)
+		newW := max(1, int(float64(imgW)*scale))
+		newH := max(1, int(float64(imgH)*scale))
 
 		return img.Thumbnail(newW, newH, vips.InterestingNone)