diff --git a/pkg/services/ngalert/api/tooling/definitions/prom.go b/pkg/services/ngalert/api/tooling/definitions/prom.go
index bdbe93c9c96..59bc32e041f 100644
--- a/pkg/services/ngalert/api/tooling/definitions/prom.go
+++ b/pkg/services/ngalert/api/tooling/definitions/prom.go
@@ -250,6 +250,11 @@ func (by AlertsBy) TopK(alerts []Alert, k int) []Alert {
 	// which is important for sorting alerts, as the comparison function is
 	// very expensive.
 
+	// If k is zero or less, return nothing.
+	if k < 1 {
+		return []Alert{}
+	}
+
 	// The heap must be in ascending order, so that the root of the heap is
 	// the current smallest element.
 	byAscending := func(a1, a2 *Alert) bool { return by(a2, a1) }
diff --git a/pkg/services/ngalert/api/tooling/definitions/prom_test.go b/pkg/services/ngalert/api/tooling/definitions/prom_test.go
index 2c1e60c76a2..a2013541e2b 100644
--- a/pkg/services/ngalert/api/tooling/definitions/prom_test.go
+++ b/pkg/services/ngalert/api/tooling/definitions/prom_test.go
@@ -113,6 +113,11 @@ func TestTopKAlertsByImportance(t *testing.T) {
 		input    []Alert
 		expected []Alert
 	}{{
+		name:     "no alerts are returned (k=0)",
+		k:        0,
+		input:    []Alert{{State: "normal"}, {State: "nodata"}, {State: "error"}, {State: "pending"}, {State: "alerting"}},
+		expected: []Alert{},
+	}, {
 		name:     "alerts are ordered in expected importance (k=1)",
 		k:        1,
 		input:    []Alert{{State: "normal"}, {State: "nodata"}, {State: "error"}, {State: "pending"}, {State: "alerting"}},