diff --git a/src/py_build_cmake/build.py b/src/py_build_cmake/build.py
index 9778515..3e2011d 100644
--- a/src/py_build_cmake/build.py
+++ b/src/py_build_cmake/build.py
@@ -230,11 +230,12 @@ def create_wheel(self, wheel_directory, tmp_build_dir, cfg, dist_name,
         libdir = 'purelib' if pure else 'platlib'
         paths = {'prefix': str(tmp_build_dir), libdir: str(tmp_build_dir)}
         whl.dirname = wheel_directory
-        tags = None
-        if cfg.cross:
-            tags = self.get_cross_tags(cfg.cross)
         if pure:
             tags = {'pyver': ['py3']}
+        elif cfg.cross:
+            tags = self.get_cross_tags(cfg.cross)
+        else:
+            tags = self.get_native_tags()
         wheel_path = whl.build(paths, tags=tags, wheel_version=(1, 0))
         whl_name = os.path.relpath(wheel_path, wheel_directory)
         return whl_name
@@ -532,18 +533,25 @@ def get_cross_tags(crosscfg):
             'arch': [crosscfg['arch']],
         }
 
+    @staticmethod
+    def get_native_tags():
+        from .tags import get_python_tag, get_abi_tag, get_platform_tag
+        return {
+            'pyver': [get_python_tag()],
+            'abi': [get_abi_tag()],
+            'arch': [get_platform_tag()],
+        }
+
     @staticmethod
     def get_build_config_name(cross_cfg):
         """Get a string representing the Python version, ABI and architecture,
         used to name the build folder so builds for different versions don't
         interfere."""
         if cross_cfg:
-            return '-'.join(
-                map(lambda x: x[0],
-                    _BuildBackend.get_cross_tags(cross_cfg).values()))
+            tags = _BuildBackend.get_cross_tags(cross_cfg)
         else:
-            from distlib.wheel import IMPVER, ABI, ARCH
-            return '-'.join([IMPVER, ABI, ARCH])
+            tags = _BuildBackend.get_native_tags()
+        return '-'.join(map(lambda x: x[0], tags.values()))
 
     def needs_cross_native_build(self, cfg):
         return cfg.cross and 'copy_from_native_build' in cfg.cross
diff --git a/src/py_build_cmake/tags.py b/src/py_build_cmake/tags.py
new file mode 100644
index 0000000..c38ce34
--- /dev/null
+++ b/src/py_build_cmake/tags.py
@@ -0,0 +1,83 @@
+"""
+distlib.wheel doesn't always return the correct tags, and packaging.tags
+returns all tags supported by the interpreter, not the tags that should be used
+for the generated wheels. Therefore the only option here is to write our own
+(kind of hacky) functions based on packaging.tags.
+"""
+
+from typing import Dict
+import sys
+import sysconfig
+from importlib.machinery import EXTENSION_SUFFIXES
+from distlib.util import get_platform as get_platform_dashes
+
+_INTERPRETER_SHORT_NAMES: Dict[str, str] = {
+    "python": "py",
+    "cpython": "cp",
+    "pypy": "pp",
+    "ironpython": "ip",
+    "jython": "jy",
+}
+
+
+def _normalize_string(s: str) -> str:
+    return s.replace(".", "_").replace("-", "_")
+
+
+def get_platform_tag() -> str:
+    return _normalize_string(get_platform_dashes())
+
+
+def get_interpreter_name() -> str:
+    name = sys.implementation.name
+    return _INTERPRETER_SHORT_NAMES.get(name) or name
+
+
+def get_interpreter_version() -> str:
+    return "".join(map(str, sys.version_info[:2]))
+
+
+def get_cpython_interpreter() -> str:
+    return f"cp{get_interpreter_version()}"
+
+
+def get_cpython_abi() -> str:
+    """
+    Get the ABI string for CPython, e.g. cp37m.
+
+    https://github.com/pypa/packaging/blob/917612f5774571a99902b5fe04d06099b9e8b667/packaging/tags.py#L135
+    """
+    py_version = sys.version_info[:2]
+    debug = pymalloc = ""
+    with_debug = sysconfig.get_config_var("Py_DEBUG")
+    has_refcount = hasattr(sys, "gettotalrefcount")
+    # Windows doesn't set Py_DEBUG, so checking for support of debug-compiled
+    # extension modules is the best option.
+    # https://github.com/pypa/pip/issues/3383#issuecomment-173267692
+    has_ext = "_d.pyd" in EXTENSION_SUFFIXES
+    if with_debug or (with_debug is None and (has_refcount or has_ext)):
+        debug = "d"
+    if py_version < (3, 8):
+        with_pymalloc = sysconfig.get_config_var("WITH_PYMALLOC")
+        if with_pymalloc or with_pymalloc is None:
+            pymalloc = "m"
+    return f"{get_cpython_interpreter()}{debug}{pymalloc}"
+
+
+def get_generic_interpreter() -> str:
+    return f"{get_interpreter_name()}{get_interpreter_version()}"
+
+
+def get_generic_abi() -> str:
+    abi = sysconfig.get_config_var("SOABI") or "none"
+    return _normalize_string(abi)
+
+
+def get_python_tag() -> str:
+    if get_interpreter_name() == "cp": return get_cpython_interpreter()
+    else: return get_generic_interpreter()
+
+
+def get_abi_tag() -> str:
+    if get_interpreter_name() == "cp": return get_cpython_abi()
+    else: return get_generic_abi()