diff --git a/scripts/jwk-precompute-params.py b/scripts/jwk-precompute-params.py
new file mode 100755
index 000000000000..c75d86f6c739
--- /dev/null
+++ b/scripts/jwk-precompute-params.py
@@ -0,0 +1,52 @@
+#!/usr/bin/env python3
+# Enhance a JWK to have all of its optional performance parameters.
+# Intended to be used on an RSA `JWT_PRIVATE_SIGNING_JWK`.
+#
+# This is needed for the change from pyjwkest to PyJWT, since the
+# former accepts a partial list of optional parameters but the latter
+# requires that they are either all present or all absent. The optional
+# parameters provide a performance boost.
+#
+# Usage: Key JSON accepted on stdin; enhanced key printed to stdout.
+
+import json
+import sys
+
+from jwt.algorithms import RSAAlgorithm
+
+
+print("Paste the key's JSON, followed by a new line and Ctrl-D:\n", file=sys.stderr)
+old_jwk_data = json.loads(sys.stdin.read())
+
+# Clear out all of the precomputed private numbers
+for param_key in ['p', 'q', 'dp', 'dq', 'qi']:
+    if param_key in old_jwk_data:
+        del old_jwk_data[param_key]
+
+# Ensure that there aren't any unexpected parameters
+expected_remaining = {'kty', 'e', 'd', 'n', 'kid', 'key_ops'}
+unexpected_params = set(old_jwk_data.keys()) - expected_remaining
+if len(unexpected_params):
+    print(
+        f"Unexpected parameters {unexpected_params} would be lost. Aborting script. "
+        "If your key has additional parameters that are unrelated to the precomputed "
+        "private numbers, then please add them to the `expected_remaining` variable "
+        "and re-run the script. Please consider making a PR as well.",
+        file=sys.stderr
+    )
+    sys.exit(1)
+
+# Recompute private numbers
+new_jwk_data = json.loads(RSAAlgorithm.to_jwk(RSAAlgorithm.from_jwk(old_jwk_data)))
+
+# Restore the kid (key ID) param, which gets lost in the process. This adds it
+# to the front of the dict. The params are actually in a really nice order in
+# the native ordering that comes out of the JWK, with metadata first, then the
+# core params (n, e, d), and then the precomputed values.
+for restore_param in ['kid']:
+    if restore_param in old_jwk_data:
+        new_jwk_data = {restore_param: old_jwk_data[restore_param], **new_jwk_data}
+
+# Pretty-print so that the kid and modulus can be confirmed easily
+print("\n\nEnhanced private key:\n", file=sys.stderr)
+print(json.dumps(new_jwk_data, indent=4))