diff --git a/TODO.md b/TODO.md
index 4b27407..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
diff --git a/internal/imageprocessor/fit_cover_internal_test.go b/internal/imageprocessor/fit_cover_internal_test.go
new file mode 100644
index 0000000..0b01211
--- /dev/null
+++ b/internal/imageprocessor/fit_cover_internal_test.go
@@ -0,0 +1,268 @@
+package imageprocessor
+
+import (
+	"bytes"
+	"image"
+	"image/color"
+	"image/png"
+	"math"
+	"testing"
+)
+
+// TestImageProcessor_FitCoverServesThinSource verifies that FitCover serves
+// a thin source at the requested size. An 8192x1 source scaled to cover
+// 8192x8192 is 8192 times as long as the output on its long side. The centre
+// of an 8192x1 source with the proportions of 1x8192 is 1/8192 of a pixel
+// wide. Each case is also turned on its side.
+func TestImageProcessor_FitCoverServesThinSource(t *testing.T) {
+	t.Parallel()
+
+	tests := []struct {
+		name                    string
+		inputWidth, inputHeight int
+		size                    Size
+	}{
+		{"8192x1 at 8192x8192", 8192, 1, Size{Width: 8192, Height: 8192}},
+		{"8192x1 at 1x8192", 8192, 1, Size{Width: 1, Height: 8192}},
+		{"1x8192 at 8192x8192", 1, 8192, Size{Width: 8192, Height: 8192}},
+		{"1x8192 at 8192x1", 1, 8192, Size{Width: 8192, Height: 1}},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			t.Parallel()
+
+			input := createTestJPEG(t, tt.inputWidth, tt.inputHeight)
+
+			result, err := New(Params{}).Process(t.Context(),
+				bytes.NewReader(input),
+				&Request{Size: tt.size, Format: FormatJPEG, FitMode: FitCover})
+			if err != nil {
+				t.Fatalf("Process() error = %v", err)
+			}
+
+			defer func() { _ = result.Content.Close() }()
+
+			t.Logf("Process() made %dx%d", result.Width, result.Height)
+
+			if result.Width != tt.size.Width || result.Height != tt.size.Height {
+				t.Errorf("Process() made %dx%d, want %dx%d",
+					result.Width, result.Height, tt.size.Width, tt.size.Height)
+			}
+		})
+	}
+}
+
+// createBandsPNG creates a PNG of three equal bands, red, green and blue,
+// side by side when it is wider than tall and top to bottom otherwise.
+func createBandsPNG(t *testing.T, width, height int) []byte {
+	t.Helper()
+
+	bands := []color.RGBA{
+		{R: 255, A: 255},
+		{G: 255, A: 255},
+		{B: 255, A: 255},
+	}
+
+	img := image.NewRGBA(image.Rect(0, 0, width, height))
+	for y := range height {
+		for x := range width {
+			band := 3 * y / height
+			if width > height {
+				band = 3 * x / width
+			}
+
+			img.Set(x, y, bands[band])
+		}
+	}
+
+	return encodePNG(t, img)
+}
+
+// TestImageProcessor_FitCoverCropsTheCentre verifies that FitCover keeps the
+// centre of the source: a 300x100 source of red, green and blue bands side
+// by side, or a 100x300 one with them top to bottom, comes out at 50x50 as
+// its green band.
+func TestImageProcessor_FitCoverCropsTheCentre(t *testing.T) {
+	t.Parallel()
+
+	tests := []struct {
+		name                    string
+		inputWidth, inputHeight int
+	}{
+		{"bands side by side", 300, 100},
+		{"bands top to bottom", 100, 300},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			t.Parallel()
+
+			input := createBandsPNG(t, tt.inputWidth, tt.inputHeight)
+
+			result, err := New(Params{}).Process(t.Context(),
+				bytes.NewReader(input),
+				&Request{
+					Size:    Size{Width: 50, Height: 50},
+					Format:  FormatPNG,
+					FitMode: FitCover,
+				})
+			if err != nil {
+				t.Fatalf("Process() error = %v", err)
+			}
+
+			defer func() { _ = result.Content.Close() }()
+
+			output, err := png.Decode(result.Content)
+			if err != nil {
+				t.Fatalf("failed to decode output: %v", err)
+			}
+
+			bounds := output.Bounds()
+			t.Logf("Process() made %dx%d", bounds.Dx(), bounds.Dy())
+
+			if bounds.Dx() != 50 || bounds.Dy() != 50 {
+				t.Fatalf("Process() made %dx%d, want 50x50",
+					bounds.Dx(), bounds.Dy())
+			}
+
+			// Resampling may blend a little of the bands beside the
+			// green one into the output's edges.
+			for y := bounds.Min.Y; y < bounds.Max.Y; y++ {
+				for x := bounds.Min.X; x < bounds.Max.X; x++ {
+					r, g, b, _ := output.At(x, y).RGBA()
+					if r>>8 > 64 || g>>8 < 192 || b>>8 > 64 {
+						t.Fatalf("output pixel %d,%d is %d,%d,%d, want green",
+							x, y, r>>8, g>>8, b>>8)
+					}
+				}
+			}
+		})
+	}
+}
+
+// The greys of createSquarePNG, and the grey halfway between them.
+const (
+	backgroundGrey = 192
+	squareGrey     = 64
+	halfwayGrey    = (backgroundGrey + squareGrey) / 2
+)
+
+// createSquarePNG creates a grey PNG side pixels square with a darker grey
+// square squareSide pixels wide in its centre.
+func createSquarePNG(t *testing.T, side, squareSide int) []byte {
+	t.Helper()
+
+	first := (side - squareSide) / 2
+	last := first + squareSide - 1
+
+	img := image.NewGray(image.Rect(0, 0, side, side))
+	for y := range side {
+		for x := range side {
+			grey := uint8(backgroundGrey)
+			if x >= first && x <= last && y >= first && y <= last {
+				grey = squareGrey
+			}
+
+			img.SetGray(x, y, color.Gray{Y: grey})
+		}
+	}
+
+	return encodePNG(t, img)
+}
+
+// squareLength returns how long the square is along greys, the greys of a
+// row or column of the output that crosses it: the distance between the
+// first and the last point where greys passes halfwayGrey, or 0 when there
+// is no such point. Resampling blurs the square's edges over several
+// pixels, and each point is placed between the two pixels on either side
+// of it in proportion to their greys, so the length is measured to a
+// fraction of a pixel.
+func squareLength(greys []float64) float64 {
+	first, last := -1.0, -1.0
+
+	for i := 1; i < len(greys); i++ {
+		before, after := greys[i-1], greys[i]
+		if (before > halfwayGrey) == (after > halfwayGrey) {
+			continue
+		}
+
+		point := float64(i-1) + (before-halfwayGrey)/(before-after)
+		if first < 0 {
+			first = point
+		}
+
+		last = point
+	}
+
+	return last - first
+}
+
+// TestImageProcessor_FitCoverKeepsProportions verifies that FitCover scales
+// both sides of the source by the same amount: a square in the centre of
+// the source comes out square. Its width and height are measured along the
+// output's middle row and column.
+func TestImageProcessor_FitCoverKeepsProportions(t *testing.T) {
+	t.Parallel()
+
+	tests := []struct {
+		name             string
+		side, squareSide int
+		size             Size
+	}{
+		{"16x16 at 100x60", 16, 8, Size{Width: 100, Height: 60}},
+		{"16x16 at 60x100", 16, 8, Size{Width: 60, Height: 100}},
+		{"10x10 at 100x35", 10, 2, Size{Width: 100, Height: 35}},
+		{"10x10 at 35x100", 10, 2, Size{Width: 35, Height: 100}},
+		{"64x64 at 300x100", 64, 16, Size{Width: 300, Height: 100}},
+		{"64x64 at 100x300", 64, 16, Size{Width: 100, Height: 300}},
+	}
+
+	for _, tt := range tests {
+		t.Run(tt.name, func(t *testing.T) {
+			t.Parallel()
+
+			input := createSquarePNG(t, tt.side, tt.squareSide)
+
+			result, err := New(Params{}).Process(t.Context(),
+				bytes.NewReader(input),
+				&Request{Size: tt.size, Format: FormatPNG, FitMode: FitCover})
+			if err != nil {
+				t.Fatalf("Process() error = %v", err)
+			}
+
+			defer func() { _ = result.Content.Close() }()
+
+			output, err := png.Decode(result.Content)
+			if err != nil {
+				t.Fatalf("failed to decode output: %v", err)
+			}
+
+			bounds := output.Bounds()
+			if bounds.Dx() != tt.size.Width || bounds.Dy() != tt.size.Height {
+				t.Fatalf("Process() made %dx%d, want %dx%d",
+					bounds.Dx(), bounds.Dy(), tt.size.Width, tt.size.Height)
+			}
+
+			row := make([]float64, bounds.Dx())
+			for x := range row {
+				r, _, _, _ := output.At(x, bounds.Dy()/2).RGBA()
+				row[x] = float64(r >> 8)
+			}
+
+			column := make([]float64, bounds.Dy())
+			for y := range column {
+				r, _, _, _ := output.At(bounds.Dx()/2, y).RGBA()
+				column[y] = float64(r >> 8)
+			}
+
+			width, height := squareLength(row), squareLength(column)
+			t.Logf("square is %.2f wide and %.2f high", width, height)
+
+			if width == 0 || math.Abs(width-height) > 0.5 {
+				t.Errorf("square is %.2f wide and %.2f high, want it square",
+					width, height)
+			}
+		})
+	}
+}
diff --git a/internal/imageprocessor/imageprocessor.go b/internal/imageprocessor/imageprocessor.go
index 2a1fbf5..716b9ad 100644
--- a/internal/imageprocessor/imageprocessor.go
+++ b/internal/imageprocessor/imageprocessor.go
@@ -475,8 +475,8 @@ func (p *ImageProcessor) resize(
 ) error {
 	switch fit {
 	case FitCover, "":
-		// Resize and crop to fill exact dimensions (default)
-		return img.Thumbnail(width, height, vips.InterestingCentre)
+		// Crop the centre and resize to fill exact dimensions (default)
+		return cropCentreAndResize(img, width, height)
 
 	case FitContain:
 		// Resize to fit within dimensions, maintaining aspect ratio
@@ -530,6 +530,38 @@ func (p *ImageProcessor) resize(
 	}
 }
 
+// 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 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 {
+		left = (imgW*height - imgH*width) / (2 * height) //nolint:mnd // each side
+	} else {
+		top = (imgH*width - imgW*height) / (2 * width) //nolint:mnd // each side
+	}
+
+	err := img.ExtractArea(left, top, imgW-2*left, imgH-2*top)
+	if err != nil {
+		return err
+	}
+
+	return img.Thumbnail(width, height, vips.InterestingCentre)
+}
+
 const defaultQuality = 85
 
 // encode encodes an image to the specified format. govips gives pixa no way