diff --git a/internal/imageprocessor/fit_outside_internal_test.go b/internal/imageprocessor/fit_outside_internal_test.go
new file mode 100644
index 0000000..ab3737f
--- /dev/null
+++ b/internal/imageprocessor/fit_outside_internal_test.go
@@ -0,0 +1,62 @@
+package imageprocessor
+
+import (
+	"bytes"
+	"errors"
+	"testing"
+)
+
+// TestImageProcessor_RefusesFitOutsideAboveMaximum verifies that FitOutside,
+// which scales the input to cover the requested size and so past it on one
+// side, is refused with ErrOutputTooLarge when that side would come out above
+// MaxOutputDimension, and otherwise makes the scaled size. A 1024x256 or
+// 256x1024 input scaled by 8 has 8192 for its long side.
+func TestImageProcessor_RefusesFitOutsideAboveMaximum(t *testing.T) {
+	t.Parallel()
+
+	tests := []struct {
+		name                    string
+		inputWidth, inputHeight int
+		size                    Size
+		// wantWidth and wantHeight are the output's, 0 for a refusal
+		wantWidth, wantHeight int
+	}{
+		{"width above the maximum", 3000, 600, Size{Width: 1, Height: 8192}, 0, 0},
+		{"height above the maximum", 600, 3000, Size{Width: 8192, Height: 1}, 0, 0},
+		{"width at the maximum", 1024, 256, Size{Width: 1, Height: 2048}, 8192, 2048},
+		{"height at the maximum", 256, 1024, Size{Width: 2048, Height: 1}, 2048, 8192},
+		{"within the maximum", 3000, 600, Size{Width: 1, Height: 1200}, 6000, 1200},
+	}
+
+	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: FitOutside})
+			if result != nil {
+				t.Logf("Process() made %dx%d", result.Width, result.Height)
+			}
+
+			if tt.wantWidth == 0 {
+				if !errors.Is(err, ErrOutputTooLarge) {
+					t.Errorf("Process() error = %v, want %v", err, ErrOutputTooLarge)
+				}
+
+				return
+			}
+
+			if err != nil {
+				t.Fatalf("Process() error = %v", err)
+			}
+
+			if result.Width != tt.wantWidth || result.Height != tt.wantHeight {
+				t.Errorf("Process() made %dx%d, want %dx%d",
+					result.Width, result.Height, tt.wantWidth, tt.wantHeight)
+			}
+		})
+	}
+}
diff --git a/internal/server/fit_outside_internal_test.go b/internal/server/fit_outside_internal_test.go
new file mode 100644
index 0000000..f0ada85
--- /dev/null
+++ b/internal/server/fit_outside_internal_test.go
@@ -0,0 +1,91 @@
+package server
+
+import (
+	"fmt"
+	"net/http"
+	"net/http/httptest"
+	"testing"
+
+	"sneak.berlin/go/pixa/internal/encurl"
+	"sneak.berlin/go/pixa/internal/imgcache"
+)
+
+// TestImageProxyRefusesFitOutsideAboveMaximum requests sizes with fit=outside
+// through both image routes. fit=outside scales the source to cover the size,
+// and so past it on one side: a size for which that side would be above 8192
+// is refused with 400 and the JSON error body, whether it is the width or the
+// height, and a size for which it stays within 8192 is served at the scaled
+// size.
+func TestImageProxyRefusesFitOutsideAboveMaximum(t *testing.T) {
+	t.Parallel()
+
+	// The upstream paths of the sources
+	const (
+		widePath   = "/wide.png"
+		rowPath    = "/row.png"
+		columnPath = "/column.png"
+	)
+
+	sources := map[string][]byte{
+		widePath:   encodeTestPNG(t, 3000, 600),
+		rowPath:    encodeTestPNG(t, 8192, 1),
+		columnPath: encodeTestPNG(t, 1, 8192),
+	}
+
+	upstream := httptest.NewServer(http.HandlerFunc(
+		func(w http.ResponseWriter, r *http.Request) {
+			w.Header().Set("Content-Type", "image/png")
+			_, _ = w.Write(sources[r.URL.Path])
+		}))
+	t.Cleanup(upstream.Close)
+
+	s, _, _ := startImageProxy(t, upstream)
+
+	generator, err := encurl.NewGenerator(testSigningKey)
+	if err != nil {
+		t.Fatalf("encurl.NewGenerator: %v", err)
+	}
+
+	tests := []struct {
+		path          string
+		width, height int
+		// wantWidth and wantHeight are the served image's, 0 for a refusal
+		wantWidth, wantHeight int
+	}{
+		{widePath, 1, 8192, 0, 0},
+		{rowPath, 1, 8192, 0, 0},
+		{columnPath, 8192, 1, 0, 0},
+		{widePath, 1, 1200, 6000, 1200},
+	}
+
+	for _, tt := range tests {
+		token, err := generator.Generate(&encurl.Payload{
+			SourceHost: upstreamHost, SourcePath: tt.path,
+			Width: tt.width, Height: tt.height, Format: imgcache.FormatJPEG,
+			FitMode: imgcache.FitOutside,
+		})
+		if err != nil {
+			t.Fatalf("encurl Generate: %v", err)
+		}
+
+		size := fmt.Sprintf("%dx%d", tt.width, tt.height)
+
+		for _, target := range []string{
+			"/v1/image/" + upstreamHost + tt.path + "/" + size +
+				".jpeg?fit=outside",
+			"/v1/e/" + token + "/img.jpg",
+		} {
+			rec := httptest.NewRecorder()
+			s.ServeHTTP(rec, httptest.NewRequestWithContext(
+				t.Context(), http.MethodGet, target, nil))
+			t.Logf("GET %s: %d, Content-Type %s",
+				target, rec.Code, rec.Header().Get("Content-Type"))
+
+			if tt.wantWidth == 0 {
+				checkSizeRefused(t, rec)
+			} else {
+				checkServedSize(t, rec, tt.wantWidth, tt.wantHeight)
+			}
+		}
+	}
+}