diff --git a/gpu/caches.go b/gpu/caches.go
index 68dffb53..12c8a505 100644
--- a/gpu/caches.go
+++ b/gpu/caches.go
@@ -6,7 +6,6 @@ import (
 	"fmt"
 
 	"gioui.org/f32"
-	"gioui.org/internal/ops"
 )
 
 type resourceCache struct {
@@ -19,7 +18,7 @@ type resourceCache struct {
 // since benchmarking showed them as a bottleneck.
 type opCache struct {
 	// store the index + 1 in cache this key is stored in
-	index map[ops.Key]int
+	index map[opKey]int
 	// list of indexes in cache that are free and can be used
 	freelist []int
 	cache    []opCacheValue
@@ -32,7 +31,7 @@ type opCacheValue struct {
 
 	bounds f32.Rectangle
 	// the fields below are handled by opCache
-	key  ops.Key
+	key  opKey
 	keep bool
 }
 
@@ -83,13 +82,13 @@ func (r *resourceCache) release() {
 
 func newOpCache() *opCache {
 	return &opCache{
-		index:    make(map[ops.Key]int),
+		index:    make(map[opKey]int),
 		freelist: make([]int, 0),
 		cache:    make([]opCacheValue, 0),
 	}
 }
 
-func (r *opCache) get(key ops.Key) (o opCacheValue, exist bool) {
+func (r *opCache) get(key opKey) (o opCacheValue, exist bool) {
 	v := r.index[key]
 	if v == 0 {
 		return
@@ -98,7 +97,7 @@ func (r *opCache) get(key ops.Key) (o opCacheValue, exist bool) {
 	return r.cache[v-1], true
 }
 
-func (r *opCache) put(key ops.Key, val opCacheValue) {
+func (r *opCache) put(key opKey, val opCacheValue) {
 	v := r.index[key]
 	val.keep = true
 	val.key = key
diff --git a/gpu/gpu.go b/gpu/gpu.go
index 9616e8af..2a1f7ca9 100644
--- a/gpu/gpu.go
+++ b/gpu/gpu.go
@@ -122,7 +122,7 @@ type pathOp struct {
 	// later clip rectangles.
 	clip      image.Rectangle
 	bounds    f32.Rectangle
-	pathKey   ops.Key
+	pathKey   opKey
 	path      bool
 	pathVerts []byte
 	parent    *pathOp
@@ -154,10 +154,15 @@ func decodeStrokeOp(data []byte) clip.StrokeStyle {
 }
 
 type quadsOp struct {
-	key ops.Key
+	key opKey
 	aux []byte
 }
 
+type opKey struct {
+	sx, hx, sy, hy float32
+	ops.Key
+}
+
 type material struct {
 	material materialType
 	opaque   bool
@@ -829,7 +834,7 @@ func (d *drawOps) newPathOp() *pathOp {
 	return &d.pathOpCache[len(d.pathOpCache)-1]
 }
 
-func (d *drawOps) addClipPath(state *drawState, aux []byte, auxKey ops.Key, bounds f32.Rectangle, off f32.Point, tr f32.Affine2D, stroke clip.StrokeStyle) {
+func (d *drawOps) addClipPath(state *drawState, aux []byte, auxKey opKey, bounds f32.Rectangle, off f32.Point, tr f32.Affine2D, stroke clip.StrokeStyle) {
 	npath := d.newPathOp()
 	*npath = pathOp{
 		parent: state.cpath,
@@ -864,6 +869,15 @@ func (d *drawOps) save(id int, state drawState) {
 	d.states[id] = state
 }
 
+func (k opKey) SetTransform(t f32.Affine2D) opKey {
+	sx, hx, _, hy, sy, _ := t.Elems()
+	k.sx = sx
+	k.hx = hx
+	k.hy = hy
+	k.sy = sy
+	return k
+}
+
 func (d *drawOps) collectOps(r *ops.Reader, state drawState) {
 	var (
 		quads quadsOp
@@ -889,7 +903,7 @@ loop:
 				break loop
 			}
 			quads.aux = encOp.Data[opconst.TypeAuxLen:]
-			quads.key = encOp.Key
+			quads.key = opKey{Key: encOp.Key}
 
 		case opconst.TypeClip:
 			var op clipOp
@@ -919,8 +933,8 @@ loop:
 				}
 			} else {
 				quads.aux, op.bounds, _ = d.boundsForTransformedRect(bounds, trans)
-				quads.key = encOp.Key
-				quads.key.SetTransform(trans)
+				quads.key = opKey{Key: encOp.Key}
+				quads.key.SetTransform(trans) // TODO: This call has no effect.
 			}
 			state.clip = state.clip.Intersect(op.bounds.Add(off))
 			d.addClipPath(&state, quads.aux, quads.key, op.bounds, off, state.t, str)
@@ -962,8 +976,9 @@ loop:
 			if clipData != nil {
 				// The paint operation is sheared or rotated, add a clip path representing
 				// this transformed rectangle.
-				encOp.Key.SetTransform(trans)
-				d.addClipPath(&state, clipData, encOp.Key, bnd, off, state.t, clip.StrokeStyle{})
+				k := opKey{Key: encOp.Key}
+				k.SetTransform(trans) // TODO: This call has no effect.
+				d.addClipPath(&state, clipData, k, bnd, off, state.t, clip.StrokeStyle{})
 			}
 
 			bounds := boundRectF(cl)
diff --git a/internal/ops/reader.go b/internal/ops/reader.go
index c0ed5ef4..146ffa63 100644
--- a/internal/ops/reader.go
+++ b/internal/ops/reader.go
@@ -5,7 +5,6 @@ package ops
 import (
 	"encoding/binary"
 
-	"gioui.org/f32"
 	"gioui.org/internal/opconst"
 	"gioui.org/op"
 )
@@ -29,10 +28,9 @@ type EncodedOp struct {
 
 // Key is a unique key for a given op.
 type Key struct {
-	ops            *op.Ops
-	pc             int
-	version        int
-	sx, hx, sy, hy float32
+	ops     *op.Ops
+	pc      int
+	version int
 }
 
 // Shadow of op.MacroOp.
@@ -80,15 +78,6 @@ func NewPC(ops *op.Ops) PC {
 	}
 }
 
-func (k Key) SetTransform(t f32.Affine2D) Key {
-	sx, hx, _, hy, sy, _ := t.Elems()
-	k.sx = sx
-	k.hx = hx
-	k.hy = hy
-	k.sy = sy
-	return k
-}
-
 func (r *Reader) Decode() (EncodedOp, bool) {
 	if r.ops == nil {
 		return EncodedOp{}, false