Clean up documentation and naming.
diff --git a/cryptography/hazmat/primitives/hashes.py b/cryptography/hazmat/primitives/hashes.py
index b3c626d..c71377d 100644
--- a/cryptography/hazmat/primitives/hashes.py
+++ b/cryptography/hazmat/primitives/hashes.py
@@ -55,12 +55,12 @@
         self._ctx = None
         return digest
 
-    def verify(self, sig):
-        if isinstance(sig, six.text_type):
+    def verify(self, digest):
+        if isinstance(digest, six.text_type):
             raise TypeError("Unicode-objects must be encoded before verifying")
-        digest = self.finalize()
-        if not constant_time.bytes_eq(digest, sig):
-            raise InvalidSignature("Signature did not match digest.")
+        hash_digest = self.finalize()
+        if not constant_time.bytes_eq(digest, hash_digest):
+            raise InvalidSignature("Digest did not match hash digest.")
 
 
 @utils.register_interface(interfaces.HashAlgorithm)
diff --git a/cryptography/hazmat/primitives/hmac.py b/cryptography/hazmat/primitives/hmac.py
index 8ade84a..76d658a 100644
--- a/cryptography/hazmat/primitives/hmac.py
+++ b/cryptography/hazmat/primitives/hmac.py
@@ -58,9 +58,9 @@
         self._ctx = None
         return digest
 
-    def verify(self, sig):
-        if isinstance(sig, six.text_type):
+    def verify(self, signature):
+        if isinstance(signature, six.text_type):
             raise TypeError("Unicode-objects must be encoded before verifying")
         digest = self.finalize()
-        if not constant_time.bytes_eq(digest, sig):
+        if not constant_time.bytes_eq(digest, signature):
             raise InvalidSignature("Signature did not match digest.")
diff --git a/docs/exceptions.rst b/docs/exceptions.rst
index 087066b..8be2c48 100644
--- a/docs/exceptions.rst
+++ b/docs/exceptions.rst
@@ -8,6 +8,12 @@
     This is raised when a context is used after being finalized.
 
 
+.. class:: InvalidSignature
+
+    This is raised when the verify function of a hash function does not
+    compare equal.
+
+
 .. class:: NotYetFinalized
 
     This is raised when the AEAD tag property is accessed on a context
diff --git a/docs/hazmat/primitives/cryptographic-hashes.rst b/docs/hazmat/primitives/cryptographic-hashes.rst
index 02c7b5e..f6a3f7a 100644
--- a/docs/hazmat/primitives/cryptographic-hashes.rst
+++ b/docs/hazmat/primitives/cryptographic-hashes.rst
@@ -67,12 +67,13 @@
 
         :return bytes: The message digest as bytes.
 
-    .. method:: verify(sig)
+    .. method:: verify(digest)
 
-        Finalize the current context and securely compare digest to sig.
+        Finalize the current context and securely compare that digest to ``digest``.
 
+        :param bytes digest: Received hash digest
         :raises cryptography.exceptions.AlreadyFinalized: See :meth:`finalize`
-        :raises cryptography.exceptions.InvalidSignature: If sig does not match digest
+        :raises cryptography.exceptions.InvalidSignature: If hash digest does not match digest
 
 
 .. _cryptographic-hash-algorithms:
diff --git a/docs/hazmat/primitives/hmac.rst b/docs/hazmat/primitives/hmac.rst
index b556bd6..0c19f20 100644
--- a/docs/hazmat/primitives/hmac.rst
+++ b/docs/hazmat/primitives/hmac.rst
@@ -70,9 +70,10 @@
         :return bytes: The message digest as bytes.
         :raises cryptography.exceptions.AlreadyFinalized:
 
-    .. method:: verify(sig)
+    .. method:: verify(signature)
 
-        Finalize the current context and securely compare digest to sig.
+        Finalize the current context and securely compare digest to ``signature``.
 
+        :param bytes signature: The bytes of the HMAC signature recieved.
         :raises cryptography.exceptions.AlreadyFinalized: See :meth:`finalize`
-        :raises cryptography.exceptions.InvalidSignature: If sig does not match digest
+        :raises cryptography.exceptions.InvalidSignature: If signature does not match digest