diff --git a/promql/engine.go b/promql/engine.go
index a5498bf56..f43015c74 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -751,8 +751,10 @@ func (ev *evaluator) vectorSelector(node *VectorSelector) Vector {
 		}
 		t, v := it.Values()
 
+		peek := 1
 		if !ok || t > refTime {
-			t, v, ok = it.PeekBack(1)
+			t, v, ok = it.PeekBack(peek)
+			peek += 1
 			if !ok || t < refTime-durationMilliseconds(StalenessDelta) {
 				continue
 			}
@@ -760,6 +762,21 @@ func (ev *evaluator) vectorSelector(node *VectorSelector) Vector {
 		if value.IsStaleNaN(v) {
 			continue
 		}
+		// Find timestamp before this point, within the staleness delta.
+		prevT, _, ok := it.PeekBack(peek)
+		if ok && prevT >= refTime-durationMilliseconds(StalenessDelta) {
+			interval := t - prevT
+			if interval*4+interval/10 < refTime-t {
+				// It is more than 4 (+10% for safety) intervals
+				// since the last data point, skip as stale.
+				//
+				// We need 4 to allow for federation, as with a 10s einterval an eval
+				// started at t=10 could be ingested at t=20, scraped for federation at
+				// t=30 and only ingested by federation at t=40.
+				continue
+			}
+		}
+
 		vec = append(vec, Sample{
 			Metric: node.series[i].Labels(),
 			Point:  Point{V: v, T: t},
diff --git a/promql/testdata/staleness.test b/promql/testdata/staleness.test
index abb67ba0b..9c24fe31c 100644
--- a/promql/testdata/staleness.test
+++ b/promql/testdata/staleness.test
@@ -10,6 +10,15 @@ eval instant at 20s metric
 eval instant at 30s metric
   {__name__="metric"} 2
 
+eval instant at 40s metric
+  {__name__="metric"} 2
+
+# It goes stale 4 intervals + 10% after the last sample.
+eval instant at 71s metric
+  {__name__="metric"} 2
+
+eval instant at 72s metric
+
 
 # Range vector ignores stale sample.
 eval instant at 30s count_over_time(metric[1m])
@@ -22,3 +31,21 @@ eval instant at 20s count_over_time(metric[1s])
 
 eval instant at 20s count_over_time(metric[10s])
   {} 1
+
+
+clear
+
+load 10s
+  metric 0
+
+# Series with single point goes stale after 5 minutes.
+eval instant at 0s metric
+  {__name__="metric"} 0
+
+eval instant at 150s metric
+  {__name__="metric"} 0
+
+eval instant at 300s metric
+  {__name__="metric"} 0
+
+eval instant at 301s metric
diff --git a/web/federate.go b/web/federate.go
index 80068e85e..bc79ffc91 100644
--- a/web/federate.go
+++ b/web/federate.go
@@ -94,7 +94,7 @@ func (h *Handler) federation(w http.ResponseWriter, req *http.Request) {
 		if ok {
 			t, v = it.Values()
 		} else {
-			t, v, ok = it.PeekBack(0)
+			t, v, ok = it.PeekBack(1)
 			if !ok {
 				continue
 			}