diff --git a/src/cmd/compile/internal/ssa/prove.go b/src/cmd/compile/internal/ssa/prove.go
index 9fedbdbbc9..1b5989e6e5 100644
--- a/src/cmd/compile/internal/ssa/prove.go
+++ b/src/cmd/compile/internal/ssa/prove.go
@@ -1732,6 +1732,14 @@ func (ft *factsTable) flowLimit(v *Value) bool {
 			return ft.unsignedMax(v, uint64(bits.Len8(uint8(a.umax))-1))
 		}
 
+	case OpPopCount64, OpPopCount32, OpPopCount16, OpPopCount8:
+		a := ft.limits[v.Args[0].ID]
+		changingBitsCount := uint64(bits.Len64(a.umax ^ a.umin))
+		sharedLeadingMask := ^(uint64(1)<<changingBitsCount - 1)
+		fixedBits := a.umax & sharedLeadingMask
+		min := uint64(bits.OnesCount64(fixedBits))
+		return ft.unsignedMinMax(v, min, min+changingBitsCount)
+
 	case OpBitLen64:
 		a := ft.limits[v.Args[0].ID]
 		return ft.unsignedMinMax(v,
diff --git a/test/prove_popcount.go b/test/prove_popcount.go
index 430df01ec3..1fe53defb0 100644
--- a/test/prove_popcount.go
+++ b/test/prove_popcount.go
@@ -33,5 +33,28 @@ func onesCountsBounds(x uint64, ensureAllBranchesCouldHappen func() bool) int {
 	return z
 }
 
+func onesCountsTight(x uint64, ensureAllBranchesCouldHappen func() bool) int {
+	const maxv = 0xff0f
+	const minv = 0xff00
+	x = max(x, minv)
+	x = min(x, maxv)
+
+	z := bits.OnesCount64(x)
+
+	if ensureAllBranchesCouldHappen() && z > bits.OnesCount64(maxv) { // ERROR "Disproved Less64$"
+		return 42
+	}
+	if ensureAllBranchesCouldHappen() && z <= bits.OnesCount64(maxv) { // ERROR "Proved Leq64$"
+		return 4242
+	}
+	if ensureAllBranchesCouldHappen() && z < bits.OnesCount64(minv) { // ERROR "Disproved Less64$"
+		return 424242
+	}
+	if ensureAllBranchesCouldHappen() && z >= bits.OnesCount64(minv) { // ERROR "Proved Leq64$"
+		return 42424242
+	}
+	return z
+}
+
 func main() {
 }