diff --git a/TODO.md b/TODO.md
index 3817c02..ce15d30 100644
--- a/TODO.md
+++ b/TODO.md
@@ -26,7 +26,10 @@ resolved. The disk cache is now size-bounded with LRU eviction
 
 # Next Step
 
-P2: security: per-origin rate limiting
+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)
 
 # Completed Steps
 
@@ -1015,6 +1018,7 @@ P2: security: per-origin rate limiting
 
 # Future Steps
 
+- P2: security: per-origin rate limiting
 - P2: HTTP response handling
     - Last-Modified headers
 - P2: configuration
diff --git a/internal/imageprocessor/computed_side_internal_test.go b/internal/imageprocessor/computed_side_internal_test.go
index f5c3d5a..231087d 100644
--- a/internal/imageprocessor/computed_side_internal_test.go
+++ b/internal/imageprocessor/computed_side_internal_test.go
@@ -50,3 +50,69 @@ func TestImageProcessor_RefusesComputedSideAboveMaximum(t *testing.T) {
 		})
 	}
 }
+
+// TestImageProcessor_ComputedSideIsAtLeastOne verifies that, for a size with
+// one side 0, the side computed from the input's proportions is 1 where it
+// would round down to 0, and that Process makes that size in every fit mode
+// but FitOutside, which scales the input to cover the size and so can make
+// it longer. Each case checks the size targetDimensions gives before it
+// calls Process: with that side at 0, an 8192x1 input at 1300x0 makes
+// libvips ask for about 39 GB with FitCover.
+func TestImageProcessor_ComputedSideIsAtLeastOne(t *testing.T) {
+	t.Parallel()
+
+	tests := []struct {
+		name                    string
+		inputWidth, inputHeight int
+		size                    Size
+		wantWidth, wantHeight   int
+	}{
+		{"8192x1 at 100x0", 8192, 1, Size{Width: 100}, 100, 1},
+		{"8192x1 at 1300x0", 8192, 1, Size{Width: 1300}, 1300, 1},
+		{"8192x2 at 100x0", 8192, 2, Size{Width: 100}, 100, 1},
+		{"1x8192 at 0x100", 1, 8192, Size{Height: 100}, 1, 100},
+		{"1x8192 at 0x1300", 1, 8192, Size{Height: 1300}, 1, 1300},
+		{"2x8192 at 0x100", 2, 8192, Size{Height: 100}, 1, 100},
+	}
+
+	fits := []FitMode{FitCover, FitContain, FitFill, FitInside, FitOutside}
+
+	for _, tt := range tests {
+		for _, fit := range fits {
+			t.Run(tt.name+" "+string(fit), func(t *testing.T) {
+				t.Parallel()
+
+				width, height, err := targetDimensions(tt.size,
+					tt.inputWidth, tt.inputHeight)
+				if err != nil || width != tt.wantWidth || height != tt.wantHeight {
+					t.Fatalf("targetDimensions() = %dx%d, %v, want %dx%d",
+						width, height, err, tt.wantWidth, tt.wantHeight)
+				}
+
+				input := createTestJPEG(t, tt.inputWidth, tt.inputHeight)
+
+				result, err := New(Params{}).Process(t.Context(),
+					bytes.NewReader(input),
+					&Request{Size: tt.size, Format: FormatJPEG, FitMode: fit})
+				if err != nil {
+					t.Fatalf("Process() error = %v", err)
+				}
+
+				defer func() { _ = result.Content.Close() }()
+
+				t.Logf("Process() made %dx%d", result.Width, result.Height)
+
+				ok := result.Width == tt.wantWidth && result.Height == tt.wantHeight
+				if fit == FitOutside {
+					ok = result.Width >= tt.wantWidth && result.Height >= tt.wantHeight
+				}
+
+				if !ok {
+					t.Errorf("Process() made %dx%d, want %dx%d (at least, for %s)",
+						result.Width, result.Height, tt.wantWidth, tt.wantHeight,
+						FitOutside)
+				}
+			})
+		}
+	}
+}