diff --git a/src/cmd/compile/internal/ssa/cse.go b/src/cmd/compile/internal/ssa/cse.go
index 4e07c89b888..39861b6e2a5 100644
--- a/src/cmd/compile/internal/ssa/cse.go
+++ b/src/cmd/compile/internal/ssa/cse.go
@@ -39,10 +39,6 @@ func cse(f *Func) {
 			if v.Type.IsMemory() {
 				continue // memory values can never cse
 			}
-			if opcodeTable[v.Op].commutative && len(v.Args) == 2 && v.Args[1].ID < v.Args[0].ID {
-				// Order the arguments of binary commutative operations.
-				v.Args[0], v.Args[1] = v.Args[1], v.Args[0]
-			}
 			a = append(a, v)
 		}
 	}
@@ -92,6 +88,15 @@ func cse(f *Func) {
 		for i := 0; i < len(partition); i++ {
 			e := partition[i]
 
+			if opcodeTable[e[0].Op].commutative {
+				// Order the first two args before comparison.
+				for _, v := range e {
+					if valueEqClass[v.Args[0].ID] > valueEqClass[v.Args[1].ID] {
+						v.Args[0], v.Args[1] = v.Args[1], v.Args[0]
+					}
+				}
+			}
+
 			// Sort by eq class of arguments.
 			byArgClass.a = e
 			byArgClass.eqClass = valueEqClass
@@ -101,6 +106,7 @@ func cse(f *Func) {
 			splitPoints = append(splitPoints[:0], 0)
 			for j := 1; j < len(e); j++ {
 				v, w := e[j-1], e[j]
+				// Note: commutative args already correctly ordered by byArgClass.
 				eqArgs := true
 				for k, a := range v.Args {
 					b := w.Args[k]
diff --git a/test/prove.go b/test/prove.go
index 9ced6166e03..9ef8949e1c4 100644
--- a/test/prove.go
+++ b/test/prove.go
@@ -273,7 +273,7 @@ func f11c(a []int, i int) {
 
 func f11d(a []int, i int) {
 	useInt(a[2*i+7])
-	useInt(a[2*i+7])
+	useInt(a[2*i+7]) // ERROR "Proved boolean IsInBounds$"
 }
 
 func f12(a []int, b int) {
@@ -438,6 +438,19 @@ func f13i(a uint) int {
 	return 3
 }
 
+func f14(p, q *int, a []int) {
+	// This crazy ordering usually gives i1 the lowest value ID,
+	// j the middle value ID, and i2 the highest value ID.
+	// That used to confuse CSE because it ordered the args
+	// of the two + ops below differently.
+	// That in turn foiled bounds check elimination.
+	i1 := *p
+	j := *q
+	i2 := *p
+	useInt(a[i1+j])
+	useInt(a[i2+j]) // ERROR "Proved boolean IsInBounds$"
+}
+
 //go:noinline
 func useInt(a int) {
 }