diff --git a/tests/test_package.py b/tests/test_package.py
index c6de1976..06269d60 100644
--- a/tests/test_package.py
+++ b/tests/test_package.py
@@ -110,6 +110,18 @@ def test_package_signed_name_is_correct():
     assert package.signed_filename == (filename + ".asc")
 
 
+def test_package_safe_name_is_correct():
+    package = package_file.PackageFile(
+        filename="tests/fixtures/deprecated-pypirc",
+        comment=None,
+        metadata=pretend.stub(name="mosaik.SimConfig"),
+        python_version=None,
+        filetype=None,
+    )
+
+    assert package.safe_name == "mosaik.SimConfig"
+
+
 @pytest.mark.parametrize("gpg_signature", [(None), (pretend.stub())])
 def test_metadata_dictionary(gpg_signature):
     meta = pretend.stub(
diff --git a/twine/package.py b/twine/package.py
index 0b68bc9c..77621664 100644
--- a/twine/package.py
+++ b/twine/package.py
@@ -14,11 +14,11 @@
 import hashlib
 import io
 import os
+import re
 import subprocess
 from typing import Dict, NamedTuple, Optional, Sequence, Tuple, Union
 
 import importlib_metadata
-import packaging.utils
 import pkginfo
 
 from twine import exceptions
@@ -44,6 +44,14 @@
 MetadataValue = Union[str, Sequence[str]]
 
 
+def safe_name(name: str) -> str:
+    """Convert an arbitrary string to a standard distribution name.
+
+    Any runs of non-alphanumeric/. characters are replaced with a single '-'.
+    """
+    return re.sub("[^A-Za-z0-9.]+", "-", name)
+
+
 class PackageFile:
     def __init__(
         self,
@@ -59,7 +67,7 @@ def __init__(
         self.metadata = metadata
         self.python_version = python_version
         self.filetype = filetype
-        self.safe_name = packaging.utils.canonicalize_name(metadata.name)
+        self.safe_name = safe_name(metadata.name)
         self.signed_filename = self.filename + ".asc"
         self.signed_basefilename = self.basefilename + ".asc"
         self.gpg_signature: Optional[Tuple[str, bytes]] = None