diff --git a/promql/engine.go b/promql/engine.go
index 2dd010b88c..d5b4cf801c 100644
--- a/promql/engine.go
+++ b/promql/engine.go
@@ -795,9 +795,8 @@ func (ev *evaluator) vectorBinop(op itemType, lhs, rhs vector, matching *VectorM
 		panic("many-to-many only allowed for set operators")
 	}
 	var (
-		result       = vector{}
-		sigf         = signatureFunc(matching.Ignoring, matching.On...)
-		resultLabels = append(matching.On, matching.Include...)
+		result = vector{}
+		sigf   = signatureFunc(matching.Ignoring, matching.On...)
 	)
 
 	// The control flow below handles one-to-one or many-to-one matching.
@@ -851,7 +850,7 @@ func (ev *evaluator) vectorBinop(op itemType, lhs, rhs vector, matching *VectorM
 		} else if !keep {
 			continue
 		}
-		metric := resultMetric(ls.Metric, op, matching.Ignoring, resultLabels...)
+		metric := resultMetric(ls.Metric, rs.Metric, op, matching)
 
 		insertedSigs, exists := matchedSigs[sig]
 		if matching.Card == CardOneToOne {
@@ -863,7 +862,7 @@ func (ev *evaluator) vectorBinop(op itemType, lhs, rhs vector, matching *VectorM
 			// In many-to-one matching the grouping labels have to ensure a unique metric
 			// for the result vector. Check whether those labels have already been added for
 			// the same matching labels.
-			insertSig := model.SignatureForLabels(metric.Metric, matching.Include...)
+			insertSig := uint64(metric.Metric.Fingerprint())
 			if !exists {
 				insertedSigs = map[uint64]struct{}{}
 				matchedSigs[sig] = insertedSigs
@@ -902,21 +901,43 @@ func signatureFunc(ignoring bool, labels ...model.LabelName) func(m metric.Metri
 
 // resultMetric returns the metric for the given sample(s) based on the vector
 // binary operation and the matching options.
-func resultMetric(met metric.Metric, op itemType, ignoring bool, labels ...model.LabelName) metric.Metric {
-	if len(labels) == 0 || ignoring {
+func resultMetric(lhs, rhs metric.Metric, op itemType, matching *VectorMatching) metric.Metric {
+	if len(matching.On)+len(matching.Include) == 0 {
 		if shouldDropMetricName(op) {
-			met.Del(model.MetricNameLabel)
+			lhs.Del(model.MetricNameLabel)
 		}
-		for _, l := range labels {
-			met.Del(l)
+		return lhs
+	}
+	if matching.Ignoring {
+		if shouldDropMetricName(op) {
+			lhs.Del(model.MetricNameLabel)
 		}
-		return met
+		if matching.Card == CardOneToOne {
+			for _, l := range matching.On {
+				lhs.Del(l)
+			}
+		}
+		for _, ln := range matching.Include {
+			// Included labels from the `group_x` modifier are taken from the one side with Ignoring.
+			value := rhs.Metric[ln]
+			if value != "" {
+				lhs.Set(ln, rhs.Metric[ln])
+			} else {
+				lhs.Del(ln)
+			}
+		}
+		return lhs
 	}
 	// As we definitely write, creating a new metric is the easiest solution.
 	m := model.Metric{}
-	for _, ln := range labels {
-		// Included labels from the `group_x` modifier are taken from the "many"-side.
-		if v, ok := met.Metric[ln]; ok {
+	for _, ln := range matching.On {
+		if v, ok := lhs.Metric[ln]; ok {
+			m[ln] = v
+		}
+	}
+	for _, ln := range matching.Include {
+		// Included labels from the `group_x` modifier are taken from the "many"-side with On.
+		if v, ok := lhs.Metric[ln]; ok {
 			m[ln] = v
 		}
 	}
diff --git a/promql/parse.go b/promql/parse.go
index ba246d424b..b724b56d59 100644
--- a/promql/parse.go
+++ b/promql/parse.go
@@ -461,7 +461,7 @@ func (p *parser) expr() Expr {
 			returnBool = true
 		}
 
-		// Parse ON clause.
+		// Parse ON/IGNORING clause.
 		if p.peek().typ == itemOn || p.peek().typ == itemIgnoring {
 			if p.peek().typ == itemIgnoring {
 				vecMatching.Ignoring = true
@@ -470,24 +470,24 @@ func (p *parser) expr() Expr {
 			vecMatching.On = p.labels()
 
 			// Parse grouping.
-			if t := p.peek().typ; t == itemGroupLeft {
+			if t := p.peek().typ; t == itemGroupLeft || t == itemGroupRight {
 				p.next()
-				vecMatching.Card = CardManyToOne
-				vecMatching.Include = p.labels()
-			} else if t == itemGroupRight {
-				p.next()
-				vecMatching.Card = CardOneToMany
-				vecMatching.Include = p.labels()
+				if t == itemGroupLeft {
+					vecMatching.Card = CardManyToOne
+				} else {
+					vecMatching.Card = CardOneToMany
+				}
+				if p.peek().typ == itemLeftParen {
+					vecMatching.Include = p.labels()
+				} else if !vecMatching.Ignoring {
+					p.errorf("must specify labels in INCLUDE clause when using ON")
+				}
 			}
 		}
 
-		if vecMatching.Ignoring && (vecMatching.Card == CardManyToOne || vecMatching.Card == CardOneToMany) {
-			p.errorf("IGNORING not permitted with many to one matching")
-		}
-
 		for _, ln := range vecMatching.On {
 			for _, ln2 := range vecMatching.Include {
-				if ln == ln2 {
+				if ln == ln2 && !vecMatching.Ignoring {
 					p.errorf("label %q must not occur in ON and INCLUDE clause at once", ln)
 				}
 			}
diff --git a/promql/parse_test.go b/promql/parse_test.go
index 22a07a138d..db39ece5a1 100644
--- a/promql/parse_test.go
+++ b/promql/parse_test.go
@@ -250,14 +250,14 @@ var testExpr = []struct {
 		input:  "1 offset 1d",
 		fail:   true,
 		errMsg: "offset modifier must be preceded by an instant or range selector",
+	}, {
+		input:  "a - on(b) group_left d",
+		fail:   true,
+		errMsg: "must specify labels in INCLUDE clause when using ON",
 	}, {
 		input:  "a - on(b) ignoring(c) d",
 		fail:   true,
 		errMsg: "parse error at char 11: no valid expression found",
-	}, {
-		input:  "a - ignoring(b) group_left(c) d",
-		fail:   true,
-		errMsg: "parse error at char 29: IGNORING not permitted with many to one matching",
 	},
 	// Vector binary operations.
 	{
@@ -590,6 +590,52 @@ var testExpr = []struct {
 				Include: model.LabelNames{"bar"},
 			},
 		},
+	}, {
+		input: "foo / ignoring(test,blub) group_left(blub) bar",
+		expected: &BinaryExpr{
+			Op: itemDIV,
+			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:     CardManyToOne,
+				On:       model.LabelNames{"test", "blub"},
+				Include:  model.LabelNames{"blub"},
+				Ignoring: true,
+			},
+		},
+	}, {
+		input: "foo / ignoring(test,blub) group_left(bar) bar",
+		expected: &BinaryExpr{
+			Op: itemDIV,
+			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:     CardManyToOne,
+				On:       model.LabelNames{"test", "blub"},
+				Include:  model.LabelNames{"bar"},
+				Ignoring: true,
+			},
+		},
 	}, {
 		input: "foo - on(test,blub) group_right(bar,foo) bar",
 		expected: &BinaryExpr{
@@ -612,6 +658,29 @@ var testExpr = []struct {
 				Include: model.LabelNames{"bar", "foo"},
 			},
 		},
+	}, {
+		input: "foo - ignoring(test,blub) group_right(bar,foo) bar",
+		expected: &BinaryExpr{
+			Op: itemSUB,
+			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:     CardOneToMany,
+				On:       model.LabelNames{"test", "blub"},
+				Include:  model.LabelNames{"bar", "foo"},
+				Ignoring: true,
+			},
+		},
 	}, {
 		input:  "foo and 1",
 		fail:   true,
@@ -671,7 +740,7 @@ var testExpr = []struct {
 	}, {
 		input:  `http_requests{group="production"} / on(instance) group_left cpu_count{type="smp"}`,
 		fail:   true,
-		errMsg: "unexpected identifier \"cpu_count\" in grouping opts, expected \"(\"",
+		errMsg: "parse error at char 61: must specify labels in INCLUDE clause when using ON",
 	}, {
 		input:  `http_requests{group="production"} + on(instance) group_left(job,instance) cpu_count{type="smp"}`,
 		fail:   true,
diff --git a/promql/testdata/operators.test b/promql/testdata/operators.test
index 1c095ebaeb..4b505374ce 100644
--- a/promql/testdata/operators.test
+++ b/promql/testdata/operators.test
@@ -223,6 +223,9 @@ load 5m
   node_cpu{instance="def",job="node",mode="idle"} 8
   node_cpu{instance="def",job="node",mode="user"} 2
 
+load 5m
+  random{foo="bar"} 1
+
 # Copy machine role to node variable.
 eval instant at 5m node_role * on (instance,job) group_left (role) node_var
   {instance="abc",job="node",role="prometheus"} 2
@@ -230,6 +233,18 @@ eval instant at 5m node_role * on (instance,job) group_left (role) node_var
 eval instant at 5m node_var * on (instance,job) group_right (role) node_role
   {instance="abc",job="node",role="prometheus"} 2
 
+eval instant at 5m node_var * ignoring (role) group_left (role) node_role
+  {instance="abc",job="node",role="prometheus"} 2
+
+eval instant at 5m node_role * ignoring (role) group_right (role) node_var
+  {instance="abc",job="node",role="prometheus"} 2
+
+# Copy machine role to node variable with instrumentation labels.
+eval instant at 5m node_cpu * ignoring (role, mode) group_left (role) node_role
+  {instance="abc",job="node",mode="idle",role="prometheus"} 3
+  {instance="abc",job="node",mode="user",role="prometheus"} 1
+
+
 # Ratio of total.
 eval instant at 5m node_cpu / on (instance,job) group_left (mode) sum by (instance,job)(node_cpu)
   {instance="abc",job="node",mode="idle"} .75
@@ -243,3 +258,31 @@ eval instant at 5m sum by (mode, job)(node_cpu) / on (job) group_left (mode) sum
 
 eval instant at 5m sum(sum by (mode, job)(node_cpu) / on (job) group_left (mode) sum by (job)(node_cpu))
   {} 1.0
+
+
+eval instant at 5m node_cpu / ignoring (mode) group_left sum without (mode)(node_cpu)
+  {instance="abc",job="node",mode="idle"} .75
+  {instance="abc",job="node",mode="user"} .25
+  {instance="def",job="node",mode="idle"} .80
+  {instance="def",job="node",mode="user"} .20
+
+eval instant at 5m node_cpu / ignoring (mode) group_left(dummy) sum without (mode)(node_cpu)
+  {instance="abc",job="node",mode="idle"} .75
+  {instance="abc",job="node",mode="user"} .25
+  {instance="def",job="node",mode="idle"} .80
+  {instance="def",job="node",mode="user"} .20
+
+eval instant at 5m sum without (instance)(node_cpu) / ignoring (mode) group_left sum without (instance, mode)(node_cpu)
+  {job="node",mode="idle"} 0.7857142857142857
+  {job="node",mode="user"} 0.21428571428571427
+
+eval instant at 5m sum(sum without (instance)(node_cpu) / ignoring (mode) group_left sum without (instance, mode)(node_cpu))
+  {} 1.0
+
+
+# Copy over label from metric with no matching labels, without having to list cross-job target labels ('job' here).
+#eval instant at 5m node_cpu + on(dummy) group_left(foo) random
+#  {instance="abc",job="node",mode="idle",foo="bar"} 3
+#  {instance="abc",job="node",mode="user",foo="bar"} 1
+#  {instance="def",job="node",mode="idle",foo="bar"} 8
+#  {instance="def",job="node",mode="user",foo="bar"} 2