diff --git a/internal/imageprocessor/deadline_internal_test.go b/internal/imageprocessor/deadline_internal_test.go
new file mode 100644
index 0000000..4d35ad0
--- /dev/null
+++ b/internal/imageprocessor/deadline_internal_test.go
@@ -0,0 +1,90 @@
+package imageprocessor
+
+import (
+	"bytes"
+	"context"
+	"errors"
+	"io"
+	"testing"
+	"time"
+)
+
+// readerAfterDeadline is a Process input whose first Read waits until done
+// is closed, so the deadline passes after Process has taken its slot and
+// before it encodes.
+type readerAfterDeadline struct {
+	data   *bytes.Reader
+	done   <-chan struct{}
+	waited bool
+}
+
+func (r *readerAfterDeadline) Read(p []byte) (int, error) {
+	if !r.waited {
+		r.waited = true
+
+		<-r.done
+	}
+
+	return r.data.Read(p)
+}
+
+// TestProcessStopsWhenDeadlinePassed checks that Process returns
+// context.DeadlineExceeded, and holds no slot afterwards, when its context's
+// deadline has passed before it starts or while it reads its input. libvips
+// cannot stop an encode once it has begun, so Process must not begin one for
+// a request that has ended.
+func TestProcessStopsWhenDeadlinePassed(t *testing.T) {
+	t.Parallel()
+
+	input := createTestJPEG(t, 50, 50)
+
+	t.Run("before Process starts", func(t *testing.T) {
+		t.Parallel()
+
+		ctx, cancel := context.WithDeadline(t.Context(),
+			time.Now().Add(-time.Second))
+		defer cancel()
+
+		checkProcessStopsAtDeadline(ctx, t, bytes.NewReader(input))
+	})
+
+	t.Run("while Process reads its input", func(t *testing.T) {
+		t.Parallel()
+
+		ctx, cancel := context.WithTimeout(t.Context(), 100*time.Millisecond)
+		defer cancel()
+
+		checkProcessStopsAtDeadline(ctx, t, &readerAfterDeadline{
+			data: bytes.NewReader(input), done: ctx.Done(),
+		})
+	})
+}
+
+// checkProcessStopsAtDeadline runs Process on input with ctx, whose deadline
+// has passed by the time Process could encode, and fails the test unless
+// Process returns context.DeadlineExceeded and gives its slot back.
+func checkProcessStopsAtDeadline(
+	ctx context.Context, t *testing.T, input io.Reader,
+) {
+	t.Helper()
+
+	proc := New(Params{MaxConcurrentProcessing: 1})
+
+	result, err := proc.Process(ctx, input, smallJPEGRequest())
+	if result != nil {
+		t.Logf("Process() made a %dx%d image after its deadline passed",
+			result.Width, result.Height)
+
+		_ = result.Content.Close()
+	}
+
+	t.Logf("Process() error = %v", err)
+
+	if !errors.Is(err, context.DeadlineExceeded) {
+		t.Errorf("Process() error = %v, want context.DeadlineExceeded", err)
+	}
+
+	if held := len(proc.processingSemaphore); held != 0 {
+		t.Errorf("%d slots still held after Process() returned", held)
+	}
+}