diff --git a/Doc/library/hmac.rst b/Doc/library/hmac.rst
index dc994b07c35..57ac8bb1612 100644
--- a/Doc/library/hmac.rst
+++ b/Doc/library/hmac.rst
@@ -14,12 +14,13 @@
 This module implements the HMAC algorithm as described by :rfc:`2104`.
 
 
-.. function:: new(key, msg=None, digestmod=None)
+.. function:: new(key, msg=None, digestmod='')
 
    Return a new hmac object.  *key* is a bytes or bytearray object giving the
    secret key.  If *msg* is present, the method call ``update(msg)`` is made.
    *digestmod* is the digest name, digest constructor or module for the HMAC
-   object to use. It supports any name suitable to :func:`hashlib.new`.
+   object to use.  It may be any name suitable to :func:`hashlib.new`.
+   Despite its argument position, it is required.
 
    .. versionchanged:: 3.4
       Parameter *key* can be a bytes or bytearray object.
@@ -28,6 +29,8 @@ This module implements the HMAC algorithm as described by :rfc:`2104`.
 
    .. deprecated-removed:: 3.4 3.8
       MD5 as implicit default digest for *digestmod* is deprecated.
+      The digestmod parameter is now required.  Pass it as a keyword
+      argument to avoid awkwardness when you do not have an initial msg.
 
 
 .. function:: digest(key, msg, digest)
@@ -127,7 +130,6 @@ This module also provides the following helper function:
       a timing attack could theoretically reveal information about the
       types and lengths of *a* and *b*—but not their values.
 
-
    .. versionadded:: 3.3
 
 
diff --git a/Lib/hmac.py b/Lib/hmac.py
index 890eaba08e8..b769876e6f7 100644
--- a/Lib/hmac.py
+++ b/Lib/hmac.py
@@ -1,4 +1,4 @@
-"""HMAC (Keyed-Hashing for Message Authentication) Python module.
+"""HMAC (Keyed-Hashing for Message Authentication) module.
 
 Implements the HMAC algorithm as described by RFC 2104.
 """
@@ -30,23 +30,25 @@ class HMAC:
     """
     blocksize = 64  # 512-bit HMAC; can be changed in subclasses.
 
-    def __init__(self, key, msg = None, digestmod = None):
+    def __init__(self, key, msg=None, digestmod=''):
         """Create a new HMAC object.
 
-        key:       key for the keyed hash object.
-        msg:       Initial input for the hash, if provided.
-        digestmod: Required.  A module supporting PEP 247.  *OR*
-                   A hashlib constructor returning a new hash object.  *OR*
-                   A hash name suitable for hashlib.new().
+        key: bytes or buffer, key for the keyed hash object.
+        msg: bytes or buffer, Initial input for the hash or None.
+        digestmod: A hash name suitable for hashlib.new(). *OR*
+                   A hashlib constructor returning a new hash object. *OR*
+                   A module supporting PEP 247.
 
-        Note: key and msg must be a bytes or bytearray objects.
+                   Required as of 3.8, despite its position after the optional
+                   msg argument.  Passing it as a keyword argument is
+                   recommended, though not required for legacy API reasons.
         """
 
         if not isinstance(key, (bytes, bytearray)):
             raise TypeError("key: expected bytes or bytearray, but got %r" % type(key).__name__)
 
-        if digestmod is None:
-            raise ValueError('`digestmod` is required.')
+        if not digestmod:
+            raise TypeError("Missing required parameter 'digestmod'.")
 
         if callable(digestmod):
             self.digest_cons = digestmod
@@ -90,8 +92,7 @@ class HMAC:
         return "hmac-" + self.inner.name
 
     def update(self, msg):
-        """Update this hashing object with the string msg.
-        """
+        """Feed data from msg into this hashing object."""
         self.inner.update(msg)
 
     def copy(self):
@@ -119,7 +120,7 @@ class HMAC:
     def digest(self):
         """Return the hash value of this hashing object.
 
-        This returns a string containing 8-bit data.  The object is
+        This returns the hmac value as bytes.  The object is
         not altered in any way by this function; you can continue
         updating the object after calling this function.
         """
@@ -132,30 +133,34 @@ class HMAC:
         h = self._current()
         return h.hexdigest()
 
-def new(key, msg = None, digestmod = None):
+def new(key, msg=None, digestmod=''):
     """Create a new hashing object and return it.
 
-    key: The starting key for the hash.
-    msg: if available, will immediately be hashed into the object's starting
-    state.
+    key: bytes or buffer, The starting key for the hash.
+    msg: bytes or buffer, Initial input for the hash, or None.
+    digestmod: A hash name suitable for hashlib.new(). *OR*
+               A hashlib constructor returning a new hash object. *OR*
+               A module supporting PEP 247.
 
-    You can now feed arbitrary strings into the object using its update()
+               Required as of 3.8, despite its position after the optional
+               msg argument.  Passing it as a keyword argument is
+               recommended, though not required for legacy API reasons.
+
+    You can now feed arbitrary bytes into the object using its update()
     method, and can ask for the hash value at any time by calling its digest()
-    method.
+    or hexdigest() methods.
     """
     return HMAC(key, msg, digestmod)
 
 
 def digest(key, msg, digest):
-    """Fast inline implementation of HMAC
+    """Fast inline implementation of HMAC.
 
-    key:    key for the keyed hash object.
-    msg:    input message
+    key: bytes or buffer, The key for the keyed hash object.
+    msg: bytes or buffer, Input message.
     digest: A hash name suitable for hashlib.new() for best performance. *OR*
             A hashlib constructor returning a new hash object. *OR*
             A module supporting PEP 247.
-
-    Note: key and msg must be a bytes or bytearray objects.
     """
     if (_hashopenssl is not None and
             isinstance(digest, str) and digest in _openssl_md_meths):
diff --git a/Lib/test/test_hmac.py b/Lib/test/test_hmac.py
index 1bbf201727d..ea00367c802 100644
--- a/Lib/test/test_hmac.py
+++ b/Lib/test/test_hmac.py
@@ -312,10 +312,15 @@ class TestVectorsTestCase(unittest.TestCase):
                 self.fail('Expected warning about small block_size')
 
     def test_with_digestmod_no_default(self):
-        with self.assertRaises(ValueError):
+        """The digestmod parameter is required as of Python 3.8."""
+        with self.assertRaisesRegex(TypeError, r'required.*digestmod'):
             key = b"\x0b" * 16
             data = b"Hi There"
             hmac.HMAC(key, data, digestmod=None)
+        with self.assertRaisesRegex(TypeError, r'required.*digestmod'):
+            hmac.new(key, data)
+        with self.assertRaisesRegex(TypeError, r'required.*digestmod'):
+            hmac.HMAC(key, msg=data, digestmod='')
 
 
 class ConstructorTestCase(unittest.TestCase):
diff --git a/Misc/NEWS.d/next/Library/2019-10-15-09-47-40.bpo-33604.J12cWT.rst b/Misc/NEWS.d/next/Library/2019-10-15-09-47-40.bpo-33604.J12cWT.rst
new file mode 100644
index 00000000000..fbd73003cfc
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-10-15-09-47-40.bpo-33604.J12cWT.rst
@@ -0,0 +1,3 @@
+Fixed `hmac.new` and `hmac.HMAC` to raise TypeError instead of ValueError
+when the digestmod parameter, now required in 3.8, is omitted.  Also
+clarified the hmac module documentation and docstrings.