diff --git a/render/memoise.go b/render/memoise.go
index 6f96e1c397..93859327d8 100644
--- a/render/memoise.go
+++ b/render/memoise.go
@@ -27,6 +27,9 @@ type memoise struct {
 
 // Memoise wraps the renderer in a loving embrace of caching.
 func Memoise(r Renderer) Renderer {
+	if _, ok := r.(*memoise); ok {
+		return r // fixpoint
+	}
 	return &memoise{
 		Renderer: r,
 		id:       fmt.Sprintf("%x", rand.Int63()),
diff --git a/render/memoise_test.go b/render/memoise_test.go
index 9d7954ae97..79c779a362 100644
--- a/render/memoise_test.go
+++ b/render/memoise_test.go
@@ -20,6 +20,11 @@ func TestMemoise(t *testing.T) {
 		return render.Nodes{Nodes: report.Nodes{rpt.ID: report.MakeNode(rpt.ID)}}
 	})
 	m := render.Memoise(r)
+
+	if render.Memoise(m) != m {
+		t.Errorf("Memoised renderers should be fixpoints.")
+	}
+
 	rpt1 := report.MakeReport()
 
 	result1 := m.Render(rpt1)