diff --git a/news/7296.bugfix b/news/7296.bugfix
new file mode 100644
index 00000000000..5d617bf75db
--- /dev/null
+++ b/news/7296.bugfix
@@ -0,0 +1,5 @@
+Make sure ``pip wheel`` never outputs pure python wheels with a
+python implementation tag. Better fix/workaround for
+`#3025 <https://github.com/pypa/pip/issues/3025>`_ by
+using a per-implementation wheel cache instead of caching pure python
+wheels with an implementation tag in their name.
diff --git a/src/pip/_internal/cache.py b/src/pip/_internal/cache.py
index 7a431f9a2ed..1ed7d584cb1 100644
--- a/src/pip/_internal/cache.py
+++ b/src/pip/_internal/cache.py
@@ -8,6 +8,7 @@
 import hashlib
 import logging
 import os
+import sys
 
 from pip._vendor.packaging.utils import canonicalize_name
 
@@ -15,6 +16,7 @@
 from pip._internal.models.link import Link
 from pip._internal.models.wheel import Wheel
 from pip._internal.utils.compat import expanduser
+from pip._internal.utils.misc import interpreter_name
 from pip._internal.utils.temp_dir import TempDirectory
 from pip._internal.utils.typing import MYPY_CHECK_RUNNING
 from pip._internal.utils.urls import path_to_url
@@ -65,11 +67,23 @@ def _get_cache_path_parts(self, link):
             )
         key_url = "#".join(key_parts)
 
+        # Include interpreter name, major and minor version in cache key
+        # to cope with ill-behaved sdists that build a different wheel
+        # depending on the python version their setup.py is being run on,
+        # and don't encode the difference in compatibility tags.
+        # https://github.com/pypa/pip/issues/7296
+        key = "{}-{}.{} {}".format(
+            interpreter_name(),
+            sys.version_info[0],
+            sys.version_info[1],
+            key_url,
+        )
+
         # Encode our key url with sha224, we'll use this because it has similar
         # security properties to sha256, but with a shorter total output (and
         # thus less secure). However the differences don't make a lot of
         # difference for our use case here.
-        hashed = hashlib.sha224(key_url.encode()).hexdigest()
+        hashed = hashlib.sha224(key.encode()).hexdigest()
 
         # We want to nest the directories some to prevent having a ton of top
         # level directories where we might run out of sub directories on some
diff --git a/src/pip/_internal/utils/misc.py b/src/pip/_internal/utils/misc.py
index 85acab856b0..9a802556269 100644
--- a/src/pip/_internal/utils/misc.py
+++ b/src/pip/_internal/utils/misc.py
@@ -11,6 +11,7 @@
 import io
 import logging
 import os
+import platform
 import posixpath
 import shutil
 import stat
@@ -879,3 +880,13 @@ def hash_file(path, blocksize=1 << 20):
             length += len(block)
             h.update(block)
     return (h, length)  # type: ignore
+
+
+def interpreter_name():
+    # type: () -> str
+    try:
+        name = sys.implementation.name  # type: ignore
+    except AttributeError:  # pragma: no cover
+        # Python 2.7 compatibility.
+        name = platform.python_implementation().lower()
+    return name
diff --git a/src/pip/_internal/wheel_builder.py b/src/pip/_internal/wheel_builder.py
index 994b2f1a3dc..9a408a3dbf8 100644
--- a/src/pip/_internal/wheel_builder.py
+++ b/src/pip/_internal/wheel_builder.py
@@ -9,7 +9,6 @@
 import re
 import shutil
 
-from pip._internal import pep425tags
 from pip._internal.models.link import Link
 from pip._internal.utils.logging import indent_log
 from pip._internal.utils.marker_files import has_delete_marker_file
@@ -447,10 +446,6 @@ def build(
             ', '.join([req.name for (req, _) in buildset]),
         )
 
-        python_tag = None
-        if should_unpack:
-            python_tag = pep425tags.implementation_tag
-
         with indent_log():
             build_success, build_failure = [], []
             for req, output_dir in buildset:
@@ -464,10 +459,7 @@ def build(
                     build_failure.append(req)
                     continue
 
-                wheel_file = self._build_one(
-                    req, output_dir,
-                    python_tag=python_tag,
-                )
+                wheel_file = self._build_one(req, output_dir)
                 if wheel_file:
                     if should_unpack:
                         # XXX: This is mildly duplicative with prepare_files,
diff --git a/tests/functional/test_install.py b/tests/functional/test_install.py
index ffc3736ba06..6b62d863545 100644
--- a/tests/functional/test_install.py
+++ b/tests/functional/test_install.py
@@ -12,7 +12,6 @@
 from pip._vendor.six import PY2
 
 from pip import __version__ as pip_current_version
-from pip._internal import pep425tags
 from pip._internal.cli.status_codes import ERROR, SUCCESS
 from pip._internal.models.index import PyPI, TestPyPI
 from pip._internal.utils.misc import rmtree
@@ -1297,9 +1296,9 @@ def test_install_builds_wheels(script, data, with_wheel):
     assert "Running setup.py install for requir" not in str(res), str(res)
     # wheelbroken has to run install
     assert "Running setup.py install for wheelb" in str(res), str(res)
-    # We want to make sure we used the correct implementation tag
+    # We want to make sure pure python wheels do not have an implementation tag
     assert wheels == [
-        "Upper-2.0-{}-none-any.whl".format(pep425tags.implementation_tag),
+        "Upper-2.0-py{}-none-any.whl".format(sys.version_info[0]),
     ]