diff --git a/src/pkg/image/image.go b/src/pkg/image/image.go
index f4c38d28a6d..5ea302d0da5 100644
--- a/src/pkg/image/image.go
+++ b/src/pkg/image/image.go
@@ -548,7 +548,7 @@ func NewGray16(w, h int) *Gray16 {
 	return &Gray16{pix, w, Rectangle{ZP, Point{w, h}}}
 }
 
-// A PalettedColorModel represents a fixed palette of colors.
+// A PalettedColorModel represents a fixed palette of at most 256 colors.
 type PalettedColorModel []Color
 
 func diff(a, b uint32) uint32 {
@@ -648,7 +648,20 @@ func (p *Paletted) SubImage(r Rectangle) Image {
 
 // Opaque scans the entire image and returns whether or not it is fully opaque.
 func (p *Paletted) Opaque() bool {
-	for _, c := range p.Palette {
+	var present [256]bool
+	base := p.Rect.Min.Y * p.Stride
+	i0, i1 := base+p.Rect.Min.X, base+p.Rect.Max.X
+	for y := p.Rect.Min.Y; y < p.Rect.Max.Y; y++ {
+		for _, c := range p.Pix[i0:i1] {
+			present[c] = true
+		}
+		i0 += p.Stride
+		i1 += p.Stride
+	}
+	for i, c := range p.Palette {
+		if !present[i] {
+			continue
+		}
 		_, _, _, a := c.RGBA()
 		if a != 0xffff {
 			return false
diff --git a/src/pkg/image/image_test.go b/src/pkg/image/image_test.go
index f167f7f28d8..5469d64230d 100644
--- a/src/pkg/image/image_test.go
+++ b/src/pkg/image/image_test.go
@@ -10,6 +10,7 @@ import (
 
 type image interface {
 	Image
+	Opaque() bool
 	Set(int, int, Color)
 	SubImage(Rectangle) Image
 }
@@ -49,6 +50,10 @@ func TestImage(t *testing.T) {
 			t.Errorf("%T: at (6, 3), want a non-zero color, got %v", m, m.At(6, 3))
 			continue
 		}
+		if !m.SubImage(Rect(6, 3, 7, 4)).(image).Opaque() {
+			t.Errorf("%T: at (6, 3) was not opaque", m)
+			continue
+		}
 		m = m.SubImage(Rect(3, 2, 9, 8)).(image)
 		if !Rect(3, 2, 9, 8).Eq(m.Bounds()) {
 			t.Errorf("%T: sub-image want bounds %v, got %v", m, Rect(3, 2, 9, 8), m.Bounds())