diff --git a/prometheus/registry.go b/prometheus/registry.go
index f2fb67a..6c32516 100644
--- a/prometheus/registry.go
+++ b/prometheus/registry.go
@@ -325,9 +325,17 @@ func (r *Registry) Register(c Collector) error {
 		return nil
 	}
 	if existing, exists := r.collectorsByID[collectorID]; exists {
-		return AlreadyRegisteredError{
-			ExistingCollector: existing,
-			NewCollector:      c,
+		switch e := existing.(type) {
+		case *wrappingCollector:
+			return AlreadyRegisteredError{
+				ExistingCollector: e.unwrapRecursively(),
+				NewCollector:      c,
+			}
+		default:
+			return AlreadyRegisteredError{
+				ExistingCollector: e,
+				NewCollector:      c,
+			}
 		}
 	}
 	// If the collectorID is new, but at least one of the descs existed
diff --git a/prometheus/registry_test.go b/prometheus/registry_test.go
index 3324c7c..2062e67 100644
--- a/prometheus/registry_test.go
+++ b/prometheus/registry_test.go
@@ -746,37 +746,120 @@ func BenchmarkHandler(b *testing.B) {
 }
 
 func TestAlreadyRegistered(t *testing.T) {
-	reg := prometheus.NewRegistry()
 	original := prometheus.NewCounterVec(
 		prometheus.CounterOpts{
-			Name: "test",
-			Help: "help",
+			Name:        "test",
+			Help:        "help",
+			ConstLabels: prometheus.Labels{"const": "label"},
 		},
 		[]string{"foo", "bar"},
 	)
 	equalButNotSame := prometheus.NewCounterVec(
+		prometheus.CounterOpts{
+			Name:        "test",
+			Help:        "help",
+			ConstLabels: prometheus.Labels{"const": "label"},
+		},
+		[]string{"foo", "bar"},
+	)
+	originalWithoutConstLabel := prometheus.NewCounterVec(
 		prometheus.CounterOpts{
 			Name: "test",
 			Help: "help",
 		},
 		[]string{"foo", "bar"},
 	)
-	var err error
-	if err = reg.Register(original); err != nil {
-		t.Fatal(err)
+	equalButNotSameWithoutConstLabel := prometheus.NewCounterVec(
+		prometheus.CounterOpts{
+			Name: "test",
+			Help: "help",
+		},
+		[]string{"foo", "bar"},
+	)
+
+	scenarios := []struct {
+		name              string
+		originalCollector prometheus.Collector
+		registerWith      func(prometheus.Registerer) prometheus.Registerer
+		newCollector      prometheus.Collector
+		reRegisterWith    func(prometheus.Registerer) prometheus.Registerer
+	}{
+		{
+			"RegisterNormallyReregisterNormally",
+			original,
+			func(r prometheus.Registerer) prometheus.Registerer { return r },
+			equalButNotSame,
+			func(r prometheus.Registerer) prometheus.Registerer { return r },
+		},
+		{
+			"RegisterNormallyReregisterWrapped",
+			original,
+			func(r prometheus.Registerer) prometheus.Registerer { return r },
+			equalButNotSameWithoutConstLabel,
+			func(r prometheus.Registerer) prometheus.Registerer {
+				return prometheus.WrapRegistererWith(prometheus.Labels{"const": "label"}, r)
+			},
+		},
+		{
+			"RegisterWrappedReregisterWrapped",
+			originalWithoutConstLabel,
+			func(r prometheus.Registerer) prometheus.Registerer {
+				return prometheus.WrapRegistererWith(prometheus.Labels{"const": "label"}, r)
+			},
+			equalButNotSameWithoutConstLabel,
+			func(r prometheus.Registerer) prometheus.Registerer {
+				return prometheus.WrapRegistererWith(prometheus.Labels{"const": "label"}, r)
+			},
+		},
+		{
+			"RegisterWrappedReregisterNormally",
+			originalWithoutConstLabel,
+			func(r prometheus.Registerer) prometheus.Registerer {
+				return prometheus.WrapRegistererWith(prometheus.Labels{"const": "label"}, r)
+			},
+			equalButNotSame,
+			func(r prometheus.Registerer) prometheus.Registerer { return r },
+		},
+		{
+			"RegisterDoublyWrappedReregisterDoublyWrapped",
+			originalWithoutConstLabel,
+			func(r prometheus.Registerer) prometheus.Registerer {
+				return prometheus.WrapRegistererWithPrefix(
+					"wrap_",
+					prometheus.WrapRegistererWith(prometheus.Labels{"const": "label"}, r),
+				)
+			},
+			equalButNotSameWithoutConstLabel,
+			func(r prometheus.Registerer) prometheus.Registerer {
+				return prometheus.WrapRegistererWithPrefix(
+					"wrap_",
+					prometheus.WrapRegistererWith(prometheus.Labels{"const": "label"}, r),
+				)
+			},
+		},
 	}
-	if err = reg.Register(equalButNotSame); err == nil {
-		t.Fatal("expected error when registering equal collector")
-	}
-	if are, ok := err.(prometheus.AlreadyRegisteredError); ok {
-		if are.ExistingCollector != original {
-			t.Error("expected original collector but got something else")
-		}
-		if are.ExistingCollector == equalButNotSame {
-			t.Error("expected original callector but got new one")
-		}
-	} else {
-		t.Error("unexpected error:", err)
+
+	for _, s := range scenarios {
+		t.Run(s.name, func(t *testing.T) {
+			var err error
+			reg := prometheus.NewRegistry()
+			if err = s.registerWith(reg).Register(s.originalCollector); err != nil {
+				t.Fatal(err)
+			}
+			if err = s.reRegisterWith(reg).Register(s.newCollector); err == nil {
+				t.Fatal("expected error when registering new collector")
+			}
+			if are, ok := err.(prometheus.AlreadyRegisteredError); ok {
+				if are.ExistingCollector != s.originalCollector {
+					t.Error("expected original collector but got something else")
+				}
+				if are.ExistingCollector == s.newCollector {
+					t.Error("expected original collector but got new one")
+				}
+			} else {
+				t.Error("unexpected error:", err)
+			}
+		})
 	}
 }
 
diff --git a/prometheus/wrap.go b/prometheus/wrap.go
index 49159bf..e303eef 100644
--- a/prometheus/wrap.go
+++ b/prometheus/wrap.go
@@ -32,6 +32,12 @@ import (
 // WrapRegistererWith provides a way to add fixed labels to a subset of
 // Collectors. It should not be used to add fixed labels to all metrics exposed.
 //
+// Conflicts between Collectors registered through the original Registerer with
+// Collectors registered through the wrapping Registerer will still be
+// detected. Any AlreadyRegisteredError returned by the Register method of
+// either Registerer will contain the ExistingCollector in the form it was
+// provided to the respective registry.
+//
 // The Collector example demonstrates a use of WrapRegistererWith.
 func WrapRegistererWith(labels Labels, reg Registerer) Registerer {
 	return &wrappingRegisterer{
@@ -54,6 +60,12 @@ func WrapRegistererWith(labels Labels, reg Registerer) Registerer {
 // (see NewGoCollector) and the process collector (see NewProcessCollector). (In
 // fact, those metrics are already prefixed with “go_” or “process_”,
 // respectively.)
+//
+// Conflicts between Collectors registered through the original Registerer with
+// Collectors registered through the wrapping Registerer will still be
+// detected. Any AlreadyRegisteredError returned by the Register method of
+// either Registerer will contain the ExistingCollector in the form it was
+// provided to the respective registry.
 func WrapRegistererWithPrefix(prefix string, reg Registerer) Registerer {
 	return &wrappingRegisterer{
 		wrappedRegisterer: reg,
@@ -123,6 +135,15 @@ func (c *wrappingCollector) Describe(ch chan<- *Desc) {
 	}
 }
 
+func (c *wrappingCollector) unwrapRecursively() Collector {
+	switch wc := c.wrappedCollector.(type) {
+	case *wrappingCollector:
+		return wc.unwrapRecursively()
+	default:
+		return wc
+	}
+}
+
 type wrappingMetric struct {
 	wrappedMetric Metric
 	prefix        string