diff --git a/internal/imageprocessor/fit_cover_internal_test.go b/internal/imageprocessor/fit_cover_internal_test.go
index 38e8db6..0b01211 100644
--- a/internal/imageprocessor/fit_cover_internal_test.go
+++ b/internal/imageprocessor/fit_cover_internal_test.go
@@ -5,6 +5,7 @@ import (
 	"image"
 	"image/color"
 	"image/png"
+	"math"
 	"testing"
 )
 
@@ -139,3 +140,129 @@ func TestImageProcessor_FitCoverCropsTheCentre(t *testing.T) {
 		})
 	}
 }
+
+// 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)
+			}
+		})
+	}
+}