diff --git a/rtmp/amf/amf_test.go b/rtmp/amf/amf_test.go
index 04cc1ebc..437e49c9 100644
--- a/rtmp/amf/amf_test.go
+++ b/rtmp/amf/amf_test.go
@@ -57,12 +57,12 @@ func TestSanity(t *testing.T) {
 
 // TestStrings tests string encoding and decoding.
 func TestStrings(t *testing.T) {
+	// Short string encoding is as follows:
+	//   enc[0]   = data type (typeString)
+	//   end[1:3] = size
+	//   enc[3:]  = data
 	for _, s := range testStrings {
-		// Short string encoding is as follows:
-		//   enc[0]   = data type (typeString)
-		//   end[1:3] = size
-		//   enc[3:]  = data
-		buf := make([]byte, len(s)+5)
+		buf := make([]byte, len(s)+7)
 		_, err := EncodeString(buf, s)
 		if err != nil {
 			t.Errorf("EncodeString failed")
@@ -75,10 +75,26 @@ func TestStrings(t *testing.T) {
 			t.Errorf("DecodeString did not produce original string, got %v", ds)
 		}
 	}
+	// Long string encoding is as follows:
+	//   enc[0]   = data type (typeString)
+	//   end[1:5] = size
+	//   enc[5:]  = data
+	s := string(make([]byte, 65536))
+	buf := make([]byte, len(s)+7)
+	_, err := EncodeString(buf, s)
+	if err != nil {
+		t.Errorf("EncodeString failed")
+	}
+	if buf[0] != typeLongString {
+		t.Errorf("Expected typeLongString, got %v", buf[0])
+	}
+	ds := DecodeLongString(buf[1:])
+	if s != ds {
+		t.Errorf("DecodeLongString did not produce original string, got %v", ds)
+	}
 }
 
-// TestNumbers tests 24-bit encoding and encoding.
-// We don't test the others as they are just wrappers for standard functions in encoding/binary.
+// TestNumbers tests number encoding and encoding.
 func TestNumbers(t *testing.T) {
 	for _, n := range testNumbers {
 		buf := make([]byte, 4) // NB: encoder requires an extra byte for some reason
@@ -90,6 +106,14 @@ func TestNumbers(t *testing.T) {
 		if n != dn {
 			t.Errorf("DecodeInt24 did not produce original Number, got %v", dn)
 		}
+		_, err = EncodeInt32(buf, n)
+		if err != nil {
+			t.Errorf("EncodeInt32 failed")
+		}
+		dn = int32(DecodeInt32(buf))
+		if n != dn {
+			t.Errorf("DecodeInt32 did not produce original Number, got %v", dn)
+		}
 	}
 }