diff --git a/dns/dnsmessage/message.go b/dns/dnsmessage/message.go
index 0ab4aab..d8d3b03 100644
--- a/dns/dnsmessage/message.go
+++ b/dns/dnsmessage/message.go
@@ -91,6 +91,7 @@
 	errTooManyAdditionals = errors.New("too many Additionals to pack (>65535)")
 	errNonCanonicalName   = errors.New("name is not in canonical format (it must end with a .)")
 	errStringTooLong      = errors.New("character string exceeds maximum length (255)")
+	errCompressedSRV      = errors.New("compressed name in SRV resource data")
 )
 
 // Internal constants.
@@ -1610,6 +1611,10 @@
 
 // unpack unpacks a domain name.
 func (n *Name) unpack(msg []byte, off int) (int, error) {
+	return n.unpackCompressed(msg, off, true /* allowCompression */)
+}
+
+func (n *Name) unpackCompressed(msg []byte, off int, allowCompression bool) (int, error) {
 	// currOff is the current working offset.
 	currOff := off
 
@@ -1645,6 +1650,9 @@
 			name = append(name, '.')
 			currOff = endOff
 		case 0xC0: // Pointer
+			if !allowCompression {
+				return off, errCompressedSRV
+			}
 			if currOff >= len(msg) {
 				return off, errInvalidPtr
 			}
@@ -2044,7 +2052,7 @@
 		return SRVResource{}, &nestedError{"Port", err}
 	}
 	var target Name
-	if _, err := target.unpack(msg, off); err != nil {
+	if _, err := target.unpackCompressed(msg, off, false /* allowCompression */); err != nil {
 		return SRVResource{}, &nestedError{"Target", err}
 	}
 	return SRVResource{priority, weight, port, target}, nil
diff --git a/dns/dnsmessage/message_test.go b/dns/dnsmessage/message_test.go
index c143d7e..052897f 100644
--- a/dns/dnsmessage/message_test.go
+++ b/dns/dnsmessage/message_test.go
@@ -158,6 +158,28 @@
 	}
 }
 
+func TestIncompressibleName(t *testing.T) {
+	name := mustNewName("example.com.")
+	compression := map[string]int{}
+	buf, err := name.pack(make([]byte, 0, 100), compression, 0)
+	if err != nil {
+		t.Fatal("First packing failed:", err)
+	}
+	buf, err = name.pack(buf, compression, 0)
+	if err != nil {
+		t.Fatal("Second packing failed:", err)
+	}
+	var n1 Name
+	off, err := n1.unpackCompressed(buf, 0, false /* allowCompression */)
+	if err != nil {
+		t.Fatal("Unpacking incompressible name without pointers failed:", err)
+	}
+	var n2 Name
+	if _, err := n2.unpackCompressed(buf, off, false /* allowCompression */); err != errCompressedSRV {
+		t.Errorf("Unpacking compressed incompressible name with pointers: got err = %v, want = %v", err, errCompressedSRV)
+	}
+}
+
 func checkErrorPrefix(err error, prefix string) bool {
 	e, ok := err.(*nestedError)
 	return ok && e.s == prefix