diff --git a/model/metric.go b/model/metric.go
index 6289f9057..a9f0d3242 100644
--- a/model/metric.go
+++ b/model/metric.go
@@ -75,6 +75,10 @@ type Metric map[LabelName]LabelValue
 // time.
 type SampleValue float64
 
+func (s SampleValue) Equal(o SampleValue) bool {
+	return s == o
+}
+
 func (s SampleValue) ToDTO() *float64 {
 	return proto.Float64(float64(s))
 }
@@ -92,6 +96,17 @@ type SamplePair struct {
 	Timestamp time.Time
 }
 
+func (s SamplePair) Equal(o SamplePair) (equal bool) {
+	switch {
+	case !s.Value.Equal(o.Value):
+		return
+	case !s.Timestamp.Equal(o.Timestamp):
+		return
+	}
+
+	return true
+}
+
 type Values []SamplePair
 
 func (v Values) Len() int {
@@ -136,6 +151,28 @@ func (v Values) InsideInterval(t time.Time) (s bool) {
 	return true
 }
 
+// TruncateBefore returns a subslice of the original such that extraneous
+// samples in the collection that occur before the provided time are
+// dropped.  The original slice is not mutated.
+func (v Values) TruncateBefore(t time.Time) (values Values) {
+	index := sort.Search(len(v), func(i int) bool {
+		timestamp := v[i].Timestamp
+
+		return timestamp.After(t) || timestamp.Equal(t)
+	})
+
+	switch index {
+	case 0:
+		values = v
+	case len(v):
+		values = v[len(v)-1:]
+	default:
+		values = v[index-1:]
+	}
+
+	return
+}
+
 func NewValuesFromDTO(dto *dto.SampleValueSeries) (v Values) {
 	for _, value := range dto.Value {
 		v = append(v, SamplePair{
diff --git a/model/metric_test.go b/model/metric_test.go
index 4aff61170..15484eecf 100644
--- a/model/metric_test.go
+++ b/model/metric_test.go
@@ -16,6 +16,7 @@ package model
 import (
 	"github.com/prometheus/prometheus/utility/test"
 	"testing"
+	"time"
 )
 
 func testMetric(t test.Tester) {
@@ -77,3 +78,162 @@ func BenchmarkMetric(b *testing.B) {
 		testMetric(b)
 	}
 }
+
+func testValues(t test.Tester) {
+	type in struct {
+		values Values
+		time   time.Time
+	}
+	instant := time.Now()
+	var scenarios = []struct {
+		in  in
+		out Values
+	}{
+		{
+			in: in{
+				time: instant,
+				values: Values{
+					{
+						Value:     0,
+						Timestamp: instant,
+					},
+					{
+						Value:     1,
+						Timestamp: instant.Add(time.Second),
+					},
+					{
+						Value:     2,
+						Timestamp: instant.Add(2 * time.Second),
+					},
+					{
+						Value:     3,
+						Timestamp: instant.Add(3 * time.Second),
+					},
+					{
+						Value:     4,
+						Timestamp: instant.Add(4 * time.Second),
+					},
+				},
+			},
+			out: Values{
+				{
+					Value:     0,
+					Timestamp: instant,
+				},
+				{
+					Value:     1,
+					Timestamp: instant.Add(time.Second),
+				},
+				{
+					Value:     2,
+					Timestamp: instant.Add(2 * time.Second),
+				},
+				{
+					Value:     3,
+					Timestamp: instant.Add(3 * time.Second),
+				},
+				{
+					Value:     4,
+					Timestamp: instant.Add(4 * time.Second),
+				},
+			},
+		},
+		{
+			in: in{
+				time: instant.Add(2 * time.Second),
+				values: Values{
+					{
+						Value:     0,
+						Timestamp: instant,
+					},
+					{
+						Value:     1,
+						Timestamp: instant.Add(time.Second),
+					},
+					{
+						Value:     2,
+						Timestamp: instant.Add(2 * time.Second),
+					},
+					{
+						Value:     3,
+						Timestamp: instant.Add(3 * time.Second),
+					},
+					{
+						Value:     4,
+						Timestamp: instant.Add(4 * time.Second),
+					},
+				},
+			},
+			out: Values{
+				{
+					Value:     1,
+					Timestamp: instant.Add(time.Second),
+				},
+				{
+					Value:     2,
+					Timestamp: instant.Add(2 * time.Second),
+				},
+				{
+					Value:     3,
+					Timestamp: instant.Add(3 * time.Second),
+				},
+				{
+					Value:     4,
+					Timestamp: instant.Add(4 * time.Second),
+				},
+			},
+		},
+		{
+			in: in{
+				time: instant.Add(5 * time.Second),
+				values: Values{
+					{
+						Value:     0,
+						Timestamp: instant,
+					},
+					{
+						Value:     1,
+						Timestamp: instant.Add(time.Second),
+					},
+					{
+						Value:     2,
+						Timestamp: instant.Add(2 * time.Second),
+					},
+					{
+						Value:     3,
+						Timestamp: instant.Add(3 * time.Second),
+					},
+					{
+						Value:     4,
+						Timestamp: instant.Add(4 * time.Second),
+					},
+				},
+			},
+			out: Values{
+				// Preserve the last value in case it needs to be used for the next set.
+				{
+					Value:     4,
+					Timestamp: instant.Add(4 * time.Second),
+				},
+			},
+		},
+	}
+
+	for i, scenario := range scenarios {
+		actual := scenario.in.values.TruncateBefore(scenario.in.time)
+
+		if len(actual) != len(scenario.out) {
+			t.Fatalf("%d. expected length of %d, got %d", i, len(scenario.out), len(actual))
+		}
+
+		for j, actualValue := range actual {
+			if !actualValue.Equal(scenario.out[j]) {
+				t.Fatalf("%d.%d. expected %s, got %s", i, j, scenario.out[j], actualValue)
+			}
+		}
+	}
+}
+
+func TestValues(t *testing.T) {
+	testValues(t)
+}
diff --git a/storage/metric/tiered.go b/storage/metric/tiered.go
index 5cf1b5bd0..5a7c447f3 100644
--- a/storage/metric/tiered.go
+++ b/storage/metric/tiered.go
@@ -422,12 +422,17 @@ func (t *tieredStorage) renderView(viewJob viewJob) {
 				targetTime = lastChunkTime
 			}
 
+			chunk = chunk.TruncateBefore(targetTime)
+
 			// For each op, extract all needed data from the current chunk.
 			out := model.Values{}
 			for _, op := range standingOps {
 				if op.CurrentTime().After(targetTime) {
 					break
 				}
+
+				chunk = chunk.TruncateBefore(*(op.CurrentTime()))
+
 				for op.CurrentTime() != nil && !op.CurrentTime().After(targetTime) {
 					out = op.ExtractSamples(chunk)
 				}