diff --git a/pkg/labels/labels.go b/pkg/labels/labels.go
index 7defc6abc..2d79dbe75 100644
--- a/pkg/labels/labels.go
+++ b/pkg/labels/labels.go
@@ -131,44 +131,46 @@ func (ls Labels) Hash() uint64 {
 }
 
 // HashForLabels returns a hash value for the labels matching the provided names.
-func (ls Labels) HashForLabels(names ...string) uint64 {
-	b := make([]byte, 0, 1024)
-
-	for _, v := range ls {
-		for _, n := range names {
-			if v.Name == n {
-				b = append(b, v.Name...)
-				b = append(b, sep)
-				b = append(b, v.Value...)
-				b = append(b, sep)
-				break
-			}
+// 'names' have to be sorted in ascending order.
+func (ls Labels) HashForLabels(b []byte, names ...string) (uint64, []byte) {
+	b = b[:0]
+	i, j := 0, 0
+	for i < len(ls) && j < len(names) {
+		if names[j] < ls[i].Name {
+			j++
+		} else if ls[i].Name < names[j] {
+			i++
+		} else {
+			b = append(b, ls[i].Name...)
+			b = append(b, sep)
+			b = append(b, ls[i].Value...)
+			b = append(b, sep)
+			i++
+			j++
 		}
 	}
-	return xxhash.Sum64(b)
+	return xxhash.Sum64(b), b
 }
 
 // HashWithoutLabels returns a hash value for all labels except those matching
 // the provided names.
-func (ls Labels) HashWithoutLabels(names ...string) uint64 {
-	b := make([]byte, 0, 1024)
-
-Outer:
-	for _, v := range ls {
-		if v.Name == MetricName {
-			continue
+// 'names' have to be sorted in ascending order.
+func (ls Labels) HashWithoutLabels(b []byte, names ...string) (uint64, []byte) {
+	b = b[:0]
+	j := 0
+	for i := range ls {
+		for j < len(names) && names[j] < ls[i].Name {
+			j++
 		}
-		for _, n := range names {
-			if v.Name == n {
-				continue Outer
-			}
+		if ls[i].Name == MetricName || (j < len(names) && ls[i].Name == names[j]) {
+			continue
 		}
-		b = append(b, v.Name...)
+		b = append(b, ls[i].Name...)
 		b = append(b, sep)
-		b = append(b, v.Value...)
+		b = append(b, ls[i].Value...)
 		b = append(b, sep)
 	}
-	return xxhash.Sum64(b)
+	return xxhash.Sum64(b), b
 }
 
 // Copy returns a copy of the labels.
diff --git a/promql/engine.go b/promql/engine.go
index ad40ff80a..ebba3eaf9 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -1523,13 +1523,17 @@ func (ev *evaluator) VectorBinop(op ItemType, lhs, rhs Vector, matching *VectorM
 // signatureFunc returns a function that calculates the signature for a metric
 // ignoring the provided labels. If on, then the given labels are only used instead.
 func signatureFunc(on bool, names ...string) func(labels.Labels) uint64 {
-	// TODO(fabxc): ensure names are sorted and then use that and sortedness
-	// of labels by names to speed up the operations below.
-	// Alternatively, inline the hashing and don't build new label sets.
+	sort.Strings(names)
 	if on {
-		return func(lset labels.Labels) uint64 { return lset.HashForLabels(names...) }
+		return func(lset labels.Labels) uint64 {
+			h, _ := lset.HashForLabels(make([]byte, 0, 1024), names...)
+			return h
+		}
+	}
+	return func(lset labels.Labels) uint64 {
+		h, _ := lset.HashWithoutLabels(make([]byte, 0, 1024), names...)
+		return h
 	}
-	return func(lset labels.Labels) uint64 { return lset.HashWithoutLabels(names...) }
 }
 
 // resultMetric returns the metric for the given sample(s) based on the Vector
@@ -1722,8 +1726,9 @@ func (ev *evaluator) aggregation(op ItemType, grouping []string, without bool, p
 		}
 	}
 
+	sort.Strings(grouping)
 	lb := labels.NewBuilder(nil)
-
+	buf := make([]byte, 0, 1024)
 	for _, s := range vec {
 		metric := s.Metric
 
@@ -1737,9 +1742,9 @@ func (ev *evaluator) aggregation(op ItemType, grouping []string, without bool, p
 			groupingKey uint64
 		)
 		if without {
-			groupingKey = metric.HashWithoutLabels(grouping...)
+			groupingKey, buf = metric.HashWithoutLabels(buf, grouping...)
 		} else {
-			groupingKey = metric.HashForLabels(grouping...)
+			groupingKey, buf = metric.HashForLabels(buf, grouping...)
 		}
 
 		group, ok := result[groupingKey]