diff --git a/promql/engine.go b/promql/engine.go
index 23a5bb93e8..33b3667146 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -20,6 +20,7 @@ import (
 	"runtime"
 	"sort"
 	"strconv"
+	"sync"
 	"time"
 
 	"github.com/prometheus/client_golang/prometheus"
@@ -524,6 +525,14 @@ type evaluator struct {
 	ctx context.Context
 
 	Timestamp int64 // time in milliseconds
+
+	finalizers []func()
+}
+
+func (ev *evaluator) close() {
+	for _, f := range ev.finalizers {
+		f()
+	}
 }
 
 // fatalf causes a panic with the input formatted into an error.
@@ -621,6 +630,7 @@ func (ev *evaluator) evalOneOf(e Expr, t1, t2 ValueType) Value {
 
 func (ev *evaluator) Eval(expr Expr) (v Value, err error) {
 	defer ev.recover(&err)
+	defer ev.close()
 	return ev.eval(expr), nil
 }
 
@@ -732,19 +742,55 @@ func (ev *evaluator) vectorSelector(node *VectorSelector) Vector {
 	return vec
 }
 
+var pointPool = sync.Pool{}
+
+func getPointSlice(sz int) []Point {
+	p := pointPool.Get()
+	if p != nil {
+		return p.([]Point)
+	}
+	return make([]Point, 0, sz)
+}
+
+func putPointSlice(p []Point) {
+	pointPool.Put(p[:0])
+}
+
+var matrixPool = sync.Pool{}
+
+func getMatrix(sz int) Matrix {
+	m := matrixPool.Get()
+	if m != nil {
+		return m.(Matrix)
+	}
+	return make(Matrix, 0, sz)
+}
+
+func putMatrix(m Matrix) {
+	matrixPool.Put(m[:0])
+}
+
 // matrixSelector evaluates a *MatrixSelector expression.
 func (ev *evaluator) matrixSelector(node *MatrixSelector) Matrix {
 	var (
 		offset = durationMilliseconds(node.Offset)
 		maxt   = ev.Timestamp - offset
 		mint   = maxt - durationMilliseconds(node.Range)
-		Matrix = make(Matrix, 0, len(node.series))
+		matrix = getMatrix(len(node.series))
+		// Write all points into a single slice to avoid lots of tiny allocations.
+		allPoints = getPointSlice(5 * len(matrix))
+	)
+
+	ev.finalizers = append(ev.finalizers,
+		func() { putPointSlice(allPoints) },
+		func() { putMatrix(matrix) },
 	)
 
 	for i, it := range node.iterators {
+		start := len(allPoints)
+
 		ss := Series{
 			Metric: node.series[i].Labels(),
-			Points: make([]Point, 0, 16),
 		}
 
 		ok := it.Seek(maxt)
@@ -760,19 +806,22 @@ func (ev *evaluator) matrixSelector(node *MatrixSelector) Matrix {
 			t, v := buf.At()
 			// Values in the buffer are guaranteed to be smaller than maxt.
 			if t >= mint {
-				ss.Points = append(ss.Points, Point{T: t, V: v})
+				allPoints = append(allPoints, Point{T: t, V: v})
 			}
 		}
 		// The seeked sample might also be in the range.
 		t, v = it.Values()
 		if t == maxt {
-			ss.Points = append(ss.Points, Point{T: t, V: v})
+			allPoints = append(allPoints, Point{T: t, V: v})
 		}
+
+		ss.Points = allPoints[start:]
+
 		if len(ss.Points) > 0 {
-			Matrix = append(Matrix, ss)
+			matrix = append(matrix, ss)
 		}
 	}
-	return Matrix
+	return matrix
 }
 
 func (ev *evaluator) VectorAnd(lhs, rhs Vector, matching *VectorMatching) Vector {
diff --git a/storage/buffer.go b/storage/buffer.go
index 3076354680..cb989764f5 100644
--- a/storage/buffer.go
+++ b/storage/buffer.go
@@ -13,11 +13,14 @@ type BufferedSeriesIterator struct {
 // NewBuffer returns a new iterator that buffers the values within the time range
 // of the current element and the duration of delta before.
 func NewBuffer(it SeriesIterator, delta int64) *BufferedSeriesIterator {
-	return &BufferedSeriesIterator{
+	bit := &BufferedSeriesIterator{
 		it:       it,
 		buf:      newSampleRing(delta, 16),
 		lastTime: math.MinInt64,
 	}
+	it.Next()
+
+	return bit
 }
 
 // PeekBack returns the previous element of the iterator. If there is none buffered,
diff --git a/storage/buffer_test.go b/storage/buffer_test.go
index e433fb9fa6..c1f34cb91c 100644
--- a/storage/buffer_test.go
+++ b/storage/buffer_test.go
@@ -124,6 +124,33 @@ func TestBufferedSeriesIterator(t *testing.T) {
 	require.False(t, it.Next(), "next succeeded unexpectedly")
 }
 
+func BenchmarkBufferedSeriesIterator(b *testing.B) {
+	var (
+		samples []sample
+		lastT   int64
+	)
+	for i := 0; i < b.N; i++ {
+		lastT += 30
+
+		samples = append(samples, sample{
+			t: lastT,
+			v: 123, // doesn't matter
+		})
+	}
+
+	// Simulate a 5 minute rate.
+	it := NewBuffer(newListSeriesIterator(samples), 5*60)
+
+	b.SetBytes(int64(b.N * 16))
+	b.ReportAllocs()
+	b.ResetTimer()
+
+	for it.Next() {
+		// scan everything
+	}
+	require.NoError(b, it.Err())
+}
+
 type mockSeriesIterator struct {
 	seek   func(int64) bool
 	values func() (int64, float64)