diff --git a/jose.py b/jose.py
index fa2859c..fe5393c 100644
--- a/jose.py
+++ b/jose.py
@@ -158,14 +158,17 @@ def encrypt(claims, jwk, adata='', add_header=None, alg='RSA-OAEP',
                 'Unsupported compression algorithm: {}'.format(compression))
         plaintext = compress(plaintext)
 
+    adata = _jwe_adata_str(adata, b64encode_url(json_encode(header)))
+
     # body encryption/hash
     ((cipher, _), key_size), ((hash_fn, _), hash_mod) = JWA[enc]
     iv = rng(AES.block_size)
     encryption_key = rng(hash_mod.digest_size)
+    enc_key = encryption_key[-hash_mod.digest_size/2:]  # first half
+    mac_key = encryption_key[:-hash_mod.digest_size/2]  # second half
 
-    ciphertext = cipher(plaintext, encryption_key[-hash_mod.digest_size/2:], iv)
-    hash = hash_fn(_jwe_hash_str(ciphertext, iv, adata),
-            encryption_key[:-hash_mod.digest_size/2], hash_mod)
+    ciphertext = cipher(plaintext, enc_key, iv)
+    hash = hash_fn(_jwe_hash_str(ciphertext, iv, adata), mac_key, hash_mod)
 
     # cek encryption
     (cipher, _), _ = JWA[alg]
@@ -209,17 +212,26 @@ def decrypt(jwe, jwk, adata='', validate_claims=True, expiry_seconds=None):
     # decrypt body
     ((_, decipher), _), ((hash_fn, _), mod) = JWA[header['enc']]
 
-    if header.get(_TEMP_VER_KEY) == _TEMP_VER:
-        plaintext = decipher(ciphertext, encryption_key[-mod.digest_size/2:], iv)
-        hash = hash_fn(_jwe_hash_str(ciphertext, iv, adata),
-                encryption_key[:-mod.digest_size/2], mod=mod)
+    enc_key = encryption_key[-mod.digest_size/2:]  # first half
+    mac_key = encryption_key[:-mod.digest_size/2]  # second half
+
+    if header.get(_TEMP_VER_KEY) == _TEMP_VER or \
+            len(encryption_key) == mod.digest_size:
+        adata = _jwe_adata_str(adata, jwe[0])
+
+        hash = hash_fn(_jwe_hash_str(ciphertext, iv, adata), mac_key, mod=mod)
+        if not const_compare(auth_tag(hash), tag):
+            raise Error('Mismatched authentication tags')
+
+        plaintext = decipher(ciphertext, enc_key, iv)
     else:
-        plaintext = decipher(ciphertext, encryption_key[:-mod.digest_size], iv)
-        hash = hash_fn(_jwe_hash_str(plaintext, iv, adata, True),
-            encryption_key[-mod.digest_size:], mod=mod)
+        enc_key = encryption_key[:-mod.digest_size]  # first half
+        mac_key = encryption_key[-mod.digest_size:]  # second half
+        plaintext = decipher(ciphertext, enc_key, iv)
+        hash = hash_fn(_jwe_hash_str(plaintext, iv, adata, True), mac_key, mod=mod)
 
-    if not const_compare(auth_tag(hash), tag):
-        raise Error('Mismatched authentication tags')
+        if not const_compare(auth_tag(hash), tag):
+            raise Error('Mismatched authentication tags')
 
     if 'zip' in header:
         try:
@@ -524,12 +536,28 @@ def _validate(claims, validate_claims, expiry_seconds):
         _check_not_before(now, not_before)
 
 
+def _jwe_adata_str(adata, header):
+    if adata == '':
+        # draft-ietf-jose-json-web-encryption-40  5.1.  Message Encryption step 14
+        # 'Let the Additional Authenticated Data encryption parameter be
+        # ASCII(Encoded Protected Header).'
+        adata = str(header)
+    else:
+        # However if a JWE AAD value is present
+        # (which can only be the case when using the JWE JSON
+        # Serialization), instead let the Additional Authenticated Data
+        # encryption parameter be ASCII(Encoded Protected Header || '.' ||
+        # BASE64URL(JWE AAD)).
+        adata = '.'.join([str(header), adata])
+    return adata
+
+
 def _jwe_hash_str(ciphertext, iv, adata='', legacy=False):
-    # http://tools.ietf.org/html/
-    # draft-ietf-jose-json-web-algorithms-24#section-5.2.2.1
     if legacy:
         return '.'.join((adata, iv, ciphertext, str(len(adata))))
-    return '.'.join((adata, iv, ciphertext, pack("!Q", len(adata) * 8)))
+    # http://tools.ietf.org/html/
+    # draft-ietf-jose-json-web-algorithms-40#section-5.2.2.1
+    return ''.join((adata, iv, ciphertext, pack("!Q", len(adata) * 8)))
 
 
 def _jws_hash_str(header, claims):
diff --git a/tests.py b/tests.py
index d502698..b49768b 100644
--- a/tests.py
+++ b/tests.py
@@ -37,9 +37,13 @@ def legacy_encrypt(claims, jwk, adata='', add_header=None, alg='RSA-OAEP',
     if compression is not None:
         header['zip'] = compression
         try:
-            (compress, _) = jose.COMPRESSION[compression]
+            if compression == 'BAD':
+                # facilitate test for bad compression algorithm
+                (compress, _) = jose.COMPRESSION['DEF']
+            else:
+                (compress, _) = jose.COMPRESSION[compression]
         except KeyError:
-            raise Error(
+            raise jose.Error(
                 'Unsupported compression algorithm: {}'.format(compression))
         plaintext = compress(plaintext)
 
@@ -274,13 +278,9 @@ def test_encrypt_invalid_compression_error(self):
             pass
 
     def test_decrypt_invalid_compression_error(self):
-        jwe = jose.encrypt(claims, rsa_pub_key, compression='DEF')
-        header = jose.b64encode_url(
-            '{"alg": "RSA-OAEP", ''"enc": "A128CBC-HS256", "__v": 1,'
-            '"zip": "BAD"}')
-
+        jwe = legacy_encrypt(claims, rsa_pub_key, compression='BAD')
         try:
-            jose.decrypt(jose.JWE(*((header,) + (jwe[1:]))), rsa_priv_key)
+            jose.decrypt(jwe, rsa_priv_key)
             self.fail()
         except jose.Error as e:
             self.assertEqual(