diff --git a/model/relabel/relabel.go b/model/relabel/relabel.go
index 8cc367bc8d6..eb79f7be21c 100644
--- a/model/relabel/relabel.go
+++ b/model/relabel/relabel.go
@@ -277,6 +277,13 @@ func relabel(cfg *Config, lb *labels.Builder) (keep bool) {
 			return false
 		}
 	case Replace:
+		// Fast path to add or delete label pair.
+		if val == "" && cfg.Regex == DefaultRelabelConfig.Regex &&
+			!varInRegexTemplate(cfg.TargetLabel) && !varInRegexTemplate(cfg.Replacement) {
+			lb.Set(cfg.TargetLabel, cfg.Replacement)
+			break
+		}
+
 		indexes := cfg.Regex.FindStringSubmatchIndex(val)
 		// If there is no match no replacement must take place.
 		if indexes == nil {
@@ -326,3 +333,7 @@ func relabel(cfg *Config, lb *labels.Builder) (keep bool) {
 
 	return true
 }
+
+func varInRegexTemplate(template string) bool {
+	return strings.Contains(template, "$")
+}
diff --git a/model/relabel/relabel_test.go b/model/relabel/relabel_test.go
index d6e5cb43ea2..0c6d41f5e37 100644
--- a/model/relabel/relabel_test.go
+++ b/model/relabel/relabel_test.go
@@ -861,6 +861,34 @@ func BenchmarkRelabel(b *testing.B) {
 				"__scrape_timeout__", "10s",
 				"job", "kubernetes-pods"),
 		},
+		{
+			name: "static label pair",
+			config: `
+        - replacement: wwwwww
+          target_label: wwwwww
+        - replacement: yyyyyyyyyyyy
+          target_label: xxxxxxxxx
+        - replacement: xxxxxxxxx
+          target_label: yyyyyyyyyyyy
+        - source_labels: ["something"]
+          target_label: with_source_labels
+          replacement: value
+        - replacement: dropped
+          target_label: ${0}
+        - replacement: ${0}
+          target_label: dropped`,
+			lbls: labels.FromStrings(
+				"abcdefg01", "hijklmn1",
+				"abcdefg02", "hijklmn2",
+				"abcdefg03", "hijklmn3",
+				"abcdefg04", "hijklmn4",
+				"abcdefg05", "hijklmn5",
+				"abcdefg06", "hijklmn6",
+				"abcdefg07", "hijklmn7",
+				"abcdefg08", "hijklmn8",
+				"job", "foo",
+			),
+		},
 	}
 	for i := range tests {
 		err := yaml.UnmarshalStrict([]byte(tests[i].config), &tests[i].cfgs)