diff --git a/promql/engine.go b/promql/engine.go
index 92da4a41d..3a9fc8fac 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -882,9 +882,9 @@ func (ev *evaluator) vectorBinop(op itemType, lhs, rhs vector, matching *VectorM
 }
 
 // signatureFunc returns a function that calculates the signature for a metric
-// based on the provided labels. If ignoring, then the given labels are ignored instead.
+// ignoring the provided labels. If on, then the given labels are only used instead.
 func signatureFunc(on bool, labels ...model.LabelName) func(m metric.Metric) uint64 {
-	if len(labels) == 0 || !on {
+	if !on {
 		return func(m metric.Metric) uint64 {
 			tmp := m.Metric.Clone()
 			for _, l := range labels {
@@ -905,9 +905,6 @@ func resultMetric(lhs, rhs metric.Metric, op itemType, matching *VectorMatching)
 	if shouldDropMetricName(op) {
 		lhs.Del(model.MetricNameLabel)
 	}
-	if len(matching.MatchingLabels)+len(matching.Include) == 0 {
-		return lhs
-	}
 	if !matching.On {
 		if matching.Card == CardOneToOne {
 			for _, l := range matching.MatchingLabels {
diff --git a/promql/parse.go b/promql/parse.go
index 057237dae..da9c383b3 100644
--- a/promql/parse.go
+++ b/promql/parse.go
@@ -671,14 +671,16 @@ func (p *parser) labels() model.LabelNames {
 	p.expect(itemLeftParen, ctx)
 
 	labels := model.LabelNames{}
-	for {
-		id := p.expect(itemIdentifier, ctx)
-		labels = append(labels, model.LabelName(id.val))
+	if p.peek().typ != itemRightParen {
+		for {
+			id := p.expect(itemIdentifier, ctx)
+			labels = append(labels, model.LabelName(id.val))
 
-		if p.peek().typ != itemComma {
-			break
+			if p.peek().typ != itemComma {
+				break
+			}
+			p.next()
 		}
-		p.next()
 	}
 	p.expect(itemRightParen, ctx)
 
diff --git a/promql/parse_test.go b/promql/parse_test.go
index 16be4382c..5e65bfd98 100644
--- a/promql/parse_test.go
+++ b/promql/parse_test.go
@@ -547,6 +547,28 @@ var testExpr = []struct {
 				On:             true,
 			},
 		},
+	}, {
+		input: "foo and on() bar",
+		expected: &BinaryExpr{
+			Op: itemLAND,
+			LHS: &VectorSelector{
+				Name: "foo",
+				LabelMatchers: metric.LabelMatchers{
+					{Type: metric.Equal, Name: model.MetricNameLabel, Value: "foo"},
+				},
+			},
+			RHS: &VectorSelector{
+				Name: "bar",
+				LabelMatchers: metric.LabelMatchers{
+					{Type: metric.Equal, Name: model.MetricNameLabel, Value: "bar"},
+				},
+			},
+			VectorMatching: &VectorMatching{
+				Card:           CardManyToMany,
+				MatchingLabels: model.LabelNames{},
+				On:             true,
+			},
+		},
 	}, {
 		input: "foo and ignoring(test,blub) bar",
 		expected: &BinaryExpr{
@@ -568,6 +590,27 @@ var testExpr = []struct {
 				MatchingLabels: model.LabelNames{"test", "blub"},
 			},
 		},
+	}, {
+		input: "foo and ignoring() bar",
+		expected: &BinaryExpr{
+			Op: itemLAND,
+			LHS: &VectorSelector{
+				Name: "foo",
+				LabelMatchers: metric.LabelMatchers{
+					{Type: metric.Equal, Name: model.MetricNameLabel, Value: "foo"},
+				},
+			},
+			RHS: &VectorSelector{
+				Name: "bar",
+				LabelMatchers: metric.LabelMatchers{
+					{Type: metric.Equal, Name: model.MetricNameLabel, Value: "bar"},
+				},
+			},
+			VectorMatching: &VectorMatching{
+				Card:           CardManyToMany,
+				MatchingLabels: model.LabelNames{},
+			},
+		},
 	}, {
 		input: "foo unless on(bar) baz",
 		expected: &BinaryExpr{
@@ -1146,6 +1189,18 @@ var testExpr = []struct {
 			},
 			Grouping: model.LabelNames{"foo"},
 		},
+	}, {
+		input: "sum by ()(some_metric)",
+		expected: &AggregateExpr{
+			Op: itemSum,
+			Expr: &VectorSelector{
+				Name: "some_metric",
+				LabelMatchers: metric.LabelMatchers{
+					{Type: metric.Equal, Name: model.MetricNameLabel, Value: "some_metric"},
+				},
+			},
+			Grouping: model.LabelNames{},
+		},
 	}, {
 		input:  `sum some_metric by (test)`,
 		fail:   true,
@@ -1154,10 +1209,6 @@ var testExpr = []struct {
 		input:  `sum (some_metric) by test`,
 		fail:   true,
 		errMsg: "unexpected identifier \"test\" in grouping opts, expected \"(\"",
-	}, {
-		input:  `sum (some_metric) by ()`,
-		fail:   true,
-		errMsg: "unexpected \")\" in grouping opts, expected identifier",
 	}, {
 		input:  `sum (some_metric) by test`,
 		fail:   true,
diff --git a/promql/testdata/aggregators.test b/promql/testdata/aggregators.test
index de4dd1e83..78bf5192d 100644
--- a/promql/testdata/aggregators.test
+++ b/promql/testdata/aggregators.test
@@ -37,6 +37,19 @@ eval instant at 50m sum without (instance) (http_requests{job="api-server"})
   {group="canary",job="api-server"} 700
   {group="production",job="api-server"} 300
 
+# Empty by.
+eval instant at 50m sum by () (http_requests{job="api-server"})
+  {} 1000
+
+# No by/without.
+eval instant at 50m sum (http_requests{job="api-server"})
+  {} 1000
+
+# Empty without.
+eval instant at 50m sum without () (http_requests{job="api-server",group="production"})
+  {group="production",job="api-server",instance="0"} 100
+  {group="production",job="api-server",instance="1"} 200
+
 # Without with mismatched and missing labels. Do not do this.
 eval instant at 50m sum without (instance) (http_requests{job="api-server"} or foo)
   {group="canary",job="api-server"} 700
diff --git a/promql/testdata/operators.test b/promql/testdata/operators.test
index 8169ff6f4..2075e77d7 100644
--- a/promql/testdata/operators.test
+++ b/promql/testdata/operators.test
@@ -329,3 +329,21 @@ eval instant at 5m node_cpu > on(job, instance) group_left(target) (threshold or
   node_cpu{instance="abc",job="node",mode="user",target="a@b.com"} 1
   node_cpu{instance="def",job="node",mode="idle"} 8
   node_cpu{instance="def",job="node",mode="user"} 2
+
+clear
+
+load 5m
+  random{foo="bar"} 2
+  metricA{baz="meh"} 3
+  metricB{baz="meh"} 4
+
+# On with no labels, for metrics with no common labels.
+eval instant at 5m random + on() metricA
+  {} 5
+
+# Ignoring with no labels is the same as no ignoring.
+eval instant at 5m metricA + ignoring() metricB
+  {baz="meh"} 7
+
+eval instant at 5m metricA + metricB
+  {baz="meh"} 7