diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index c11ce06a..81d421e2 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -19,6 +19,8 @@ Fixed
 Added
 ~~~~~
 - Add to_jwk static method to ECAlgorithm by @leonsmith in https://github.com/jpadilla/pyjwt/pull/732
+- Add ``get_algorithm_by_name`` as a method of ``PyJWS`` objects, and expose
+  the global PyJWS method as part of the public API
 
 `v2.4.0 <https://github.com/jpadilla/pyjwt/compare/2.3.0...2.4.0>`__
 -----------------------------------------------------------------------
diff --git a/jwt/__init__.py b/jwt/__init__.py
index 6b3f8ab1..a96cc6ee 100644
--- a/jwt/__init__.py
+++ b/jwt/__init__.py
@@ -1,6 +1,7 @@
 from .api_jwk import PyJWK, PyJWKSet
 from .api_jws import (
     PyJWS,
+    get_algorithm_by_name,
     get_unverified_header,
     register_algorithm,
     unregister_algorithm,
@@ -51,6 +52,7 @@
     "get_unverified_header",
     "register_algorithm",
     "unregister_algorithm",
+    "get_algorithm_by_name",
     # Exceptions
     "DecodeError",
     "ExpiredSignatureError",
diff --git a/jwt/api_jws.py b/jwt/api_jws.py
index 16ec846c..f8c8048d 100644
--- a/jwt/api_jws.py
+++ b/jwt/api_jws.py
@@ -73,6 +73,23 @@ def get_algorithms(self):
         """
         return list(self._valid_algs)
 
+    def get_algorithm_by_name(self, alg_name: str) -> Algorithm:
+        """
+        For a given string name, return the matching Algorithm object.
+
+        Example usage:
+
+        >>> jws_obj.get_algorithm_by_name("RS256")
+        """
+        try:
+            return self._algorithms[alg_name]
+        except KeyError as e:
+            if not has_crypto and alg_name in requires_cryptography:
+                raise NotImplementedError(
+                    f"Algorithm '{alg_name}' could not be found. Do you have cryptography installed?"
+                ) from e
+            raise NotImplementedError("Algorithm not supported") from e
+
     def encode(
         self,
         payload: bytes,
@@ -84,21 +101,21 @@ def encode(
     ) -> str:
         segments = []
 
-        if algorithm is None:
-            algorithm = "none"
+        # declare a new var to narrow the type for type checkers
+        algorithm_: str = algorithm if algorithm is not None else "none"
 
         # Prefer headers values if present to function parameters.
         if headers:
             headers_alg = headers.get("alg")
             if headers_alg:
-                algorithm = headers["alg"]
+                algorithm_ = headers["alg"]
 
             headers_b64 = headers.get("b64")
             if headers_b64 is False:
                 is_payload_detached = True
 
         # Header
-        header = {"typ": self.header_typ, "alg": algorithm}  # type: Dict[str, Any]
+        header = {"typ": self.header_typ, "alg": algorithm_}  # type: Dict[str, Any]
 
         if headers:
             self._validate_headers(headers)
@@ -128,17 +145,9 @@ 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)
-
-        except KeyError as e:
-            if not has_crypto and algorithm in requires_cryptography:
-                raise NotImplementedError(
-                    f"Algorithm '{algorithm}' could not be found. Do you have cryptography installed?"
-                ) from e
-            raise NotImplementedError("Algorithm not supported") from e
+        alg_obj = self.get_algorithm_by_name(algorithm_)
+        key = alg_obj.prepare_key(key)
+        signature = alg_obj.sign(signing_input, key)
 
         segments.append(base64url_encode(signature))
 
@@ -262,14 +271,13 @@ def _verify_signature(
             raise InvalidAlgorithmError("The specified alg value is not allowed")
 
         try:
-            alg_obj = self._algorithms[alg]
-            key = alg_obj.prepare_key(key)
-
-            if not alg_obj.verify(signing_input, key, signature):
-                raise InvalidSignatureError("Signature verification failed")
-
-        except KeyError as e:
+            alg_obj = self.get_algorithm_by_name(alg)
+        except NotImplementedError as e:
             raise InvalidAlgorithmError("Algorithm not supported") from e
+        key = alg_obj.prepare_key(key)
+
+        if not alg_obj.verify(signing_input, key, signature):
+            raise InvalidSignatureError("Signature verification failed")
 
     def _validate_headers(self, headers):
         if "kid" in headers:
@@ -286,4 +294,5 @@ def _validate_kid(self, kid):
 decode = _jws_global_obj.decode
 register_algorithm = _jws_global_obj.register_algorithm
 unregister_algorithm = _jws_global_obj.unregister_algorithm
+get_algorithm_by_name = _jws_global_obj.get_algorithm_by_name
 get_unverified_header = _jws_global_obj.get_unverified_header