diff --git a/jwt/api_jws.py b/jwt/api_jws.py
index 9504c9f6..fc0fa04f 100644
--- a/jwt/api_jws.py
+++ b/jwt/api_jws.py
@@ -110,11 +110,17 @@ def encode(
 
         # Segments
         signing_input = b".".join(segments)
-        try:
-            alg_obj = self._algorithms[algorithm]
-            key = alg_obj.prepare_key(key)
-            signature = alg_obj.sign(signing_input, key)
+        alg_obj = self.get_algo_by_name(algorithm)
+        key = alg_obj.prepare_key(key)
+        signature = alg_obj.sign(signing_input, key)
+
+        segments.append(base64url_encode(signature))
+
+        return b".".join(segments)
 
+    def get_algo_by_name(self, algorithm):
+        try:
+            return self._algorithms[algorithm]
         except KeyError:
             if not has_crypto and algorithm in requires_cryptography:
                 raise NotImplementedError(
@@ -124,10 +130,6 @@ def encode(
             else:
                 raise NotImplementedError("Algorithm not supported")
 
-        segments.append(base64url_encode(signature))
-
-        return b".".join(segments)
-
     def decode(
         self,
         jwt,  # type: str
diff --git a/jwt/api_jwt.py b/jwt/api_jwt.py
index 125b57a5..f447b607 100644
--- a/jwt/api_jwt.py
+++ b/jwt/api_jwt.py
@@ -15,6 +15,7 @@
     InvalidIssuerError,
     MissingRequiredClaimError,
 )
+from .jwt_payload import JWTPayload
 from .utils import merge_dict
 
 try:
@@ -91,7 +92,7 @@ def decode(
                 DeprecationWarning,
             )
 
-        payload, _, _, _ = self._load(jwt)
+        payload, signing_input, header, signature = self._load(jwt)
 
         if options is None:
             options = {"verify_signature": verify}
@@ -113,7 +114,7 @@ def decode(
             merged_options = merge_dict(self.options, options)
             self._validate_claims(payload, merged_options, **kwargs)
 
-        return payload
+        return JWTPayload(self, payload, signing_input, header, signature)
 
     def _validate_claims(
         self, payload, options, audience=None, issuer=None, leeway=0, **kwargs
diff --git a/jwt/jwt_payload.py b/jwt/jwt_payload.py
new file mode 100644
index 00000000..5135994d
--- /dev/null
+++ b/jwt/jwt_payload.py
@@ -0,0 +1,89 @@
+"""
+= JWTPayload
+
+A JWTPayload is the result of PyJWT.decode()
+
+It
+- is a dict (namely, the decoded payload)
+- has signing_input, header, and signature as attributes
+- exposes JWTPayload.compute_hash_digest(<string>)
+  which selects a hash algo (and implementation) based on the header and uses
+  it to compute a message digest
+
+
+== Design Decision: Why JWTPayload?
+
+This implementation path was chosen to handle a desire to support additional
+verification of JWTs without changing the API of pyjwt to v2.0
+
+Because JWTPayload inherits from dict, it behaves the same as the raw dict
+objects that PyJWT.decode() used to return (prior to this addition). Unless you
+check `type(PyJWT.decode()) is dict`, you likely won't see any change.
+
+It exposes the information previously hidden by PyJWT.decode to allow complex
+verification methods to be added to pyjwt client code (rather than baked into
+pyjwt itself).
+
+It also allows carefully selected methods (like compute_hash_digest) to be
+exposed which are derived from these data.
+"""
+try:
+    from cryptography.hazmat.primitives import hashes
+    from cryptography.hazmat.backends import default_backend
+
+    has_crypto = True
+except ImportError:
+    has_crypto = False
+
+
+class JWTPayload(dict):
+    """
+    A decoded JWT payload.
+    When treated directly as a dict, represents the JWT Payload (which is
+    typically what clients want).
+
+    :ivar signing_input: The signing input as a bytestring
+    :ivar header: The JWT header as a **dict**
+    :ivar signature: The JWT signature as a string
+    """
+
+    def __init__(
+        self,
+        jwt_api,
+        payload,
+        signing_input,
+        header,
+        signature,
+        *args,
+        **kwargs
+    ):
+        super(JWTPayload, self).__init__(payload, *args, **kwargs)
+        self.signing_input = signing_input
+        self.header = header
+        self.signature = signature
+
+        self._jwt_api = jwt_api
+
+    def compute_hash_digest(self, bytestr):
+        """
+        Given a bytestring, compute a hash digest of the bytestring and
+        return it, using the algorithm specified by the JWT header.
+
+        When `cryptography` is present, it will be used.
+
+        This method is necessary in order to support computation of the OIDC
+        at_hash claim.
+        """
+        algorithm = self.header.get("alg")
+        alg_obj = self._jwt_api.get_algo_by_name(algorithm)
+        hash_alg = alg_obj.hash_alg
+
+        if has_crypto and (
+            isinstance(hash_alg, type)
+            and issubclass(hash_alg, hashes.HashAlgorithm)
+        ):
+            digest = hashes.Hash(hash_alg(), backend=default_backend())
+            digest.update(bytestr)
+            return digest.finalize()
+        else:
+            return hash_alg(bytestr).digest()
diff --git a/tests/test_api_jwt.py b/tests/test_api_jwt.py
index c1759e35..de1737d8 100644
--- a/tests/test_api_jwt.py
+++ b/tests/test_api_jwt.py
@@ -1,3 +1,4 @@
+import hashlib
 import json
 import time
 from calendar import timegm
@@ -16,10 +17,21 @@
     InvalidIssuerError,
     MissingRequiredClaimError,
 )
+from jwt.utils import force_bytes
 
-from .test_api_jws import has_crypto
 from .utils import utc_timestamp
 
+try:
+    from cryptography.hazmat.backends import default_backend
+    from cryptography.hazmat.primitives.serialization import (
+        load_pem_private_key,
+        load_ssh_public_key,
+    )
+
+    has_crypto = True
+except ImportError:
+    has_crypto = False
+
 
 @pytest.fixture
 def jwt():
@@ -525,3 +537,38 @@ def test_decode_no_algorithms_verify_false(self, jwt, payload):
             pass
         else:
             assert False, "Unexpected DeprecationWarning raised."
+
+    def test_decoded_payload_can_compute_hash(self, jwt, payload):
+        secret = "secret"
+        jwt_message = jwt.encode(payload, secret, algorithm="HS256")
+        decoded_payload = jwt.decode(jwt_message, secret)
+
+        assert (
+            decoded_payload.compute_hash_digest(b"abc")
+            == hashlib.sha256(b"abc").digest()
+        )
+
+    @pytest.mark.skipif(
+        not has_crypto, reason="Can't run without cryptography library"
+    )
+    def test_decoded_payload_can_compute_hash_rsa(self, jwt, payload):
+        with open("tests/keys/testkey_rsa", "r") as rsa_priv_file:
+            priv_rsakey = load_pem_private_key(
+                force_bytes(rsa_priv_file.read()),
+                password=None,
+                backend=default_backend(),
+            )
+
+        with open("tests/keys/testkey_rsa.pub", "r") as rsa_pub_file:
+            pub_rsakey = load_ssh_public_key(
+                force_bytes(rsa_pub_file.read()), backend=default_backend()
+            )
+        jwt_message = jwt.encode(payload, priv_rsakey, algorithm="RS256")
+        decoded_payload = jwt.decode(jwt_message, pub_rsakey)
+
+        # RSA-256 still means sha256 hashing, but using the cryptography
+        # provided value
+        assert (
+            decoded_payload.compute_hash_digest(b"abc")
+            == hashlib.sha256(b"abc").digest()
+        )