diff --git a/src/fromager/pkgmetadata/pep639.py b/src/fromager/pkgmetadata/pep639.py
index 2817f4a1..b2c47c56 100644
--- a/src/fromager/pkgmetadata/pep639.py
+++ b/src/fromager/pkgmetadata/pep639.py
@@ -180,7 +180,8 @@ def _license_text_to_spdx(text: str) -> LicenseExpression:
     "License :: OSI Approved :: European Union Public Licence 1.0 (EUPL 1.0)": "EUPL-1.0",
     "License :: OSI Approved :: European Union Public Licence 1.1 (EUPL 1.1)": "EUPL-1.1",
     "License :: OSI Approved :: European Union Public Licence 1.2 (EUPL 1.2)": "EUPL-1.2",
-    "License :: OSI Approved :: GNU Affero General Public License v3": "AGPL-3.0-only",
+    # ambiguous, see PEP 639
+    "License :: OSI Approved :: GNU Affero General Public License v3": None,
     "License :: OSI Approved :: GNU Affero General Public License v3 or later (AGPLv3+)": "AGPL-3.0-or-later",
     # multiple versions
     "License :: OSI Approved :: GNU Free Documentation License (FDL)": None,
@@ -234,7 +235,8 @@ def _license_text_to_spdx(text: str) -> LicenseExpression:
     "License :: OSI Approved :: Zero-Clause BSD (0BSD)": "0BSD",
     # multiple versions: ZPL-1.1, ZPL-2.0, ZPL-2.1
     "License :: OSI Approved :: Zope Public License": None,
-    "License :: OSI Approved :: zlib/libpng License": "zlib-acknowledgement",
+    # zlib-acknowledgement is a different license that is not OSI approved
+    "License :: OSI Approved :: zlib/libpng License": "Zlib",
     "License :: Other/Proprietary License": None,
     "License :: Public Domain": None,
     "License :: Repoze Public License": None,
diff --git a/tests/test_pkgmetadata.py b/tests/test_pkgmetadata.py
index ffc9384c..ec5833e0 100644
--- a/tests/test_pkgmetadata.py
+++ b/tests/test_pkgmetadata.py
@@ -95,6 +95,8 @@ def test_project_urls_from_metadata(
         [md(license="MIT and PSF-2.0"), "MIT AND PSF-2.0"],
         [md(license="BSD 3-Clause License"), "BSD-3-Clause"],
         [md(classifiers=["License :: OSI Approved :: MIT License"]), "MIT"],
+        # OSI-approved zlib License, not zlib/libpng with Acknowledgement
+        [md(classifiers=["License :: OSI Approved :: zlib/libpng License"]), "Zlib"],
         [
             md(
                 classifiers=[
@@ -117,6 +119,12 @@ def test_license_from_metadata(metadata: Metadata, expected: str) -> None:
         (None, None, None),
         (None, "invalid", None),
         (None, None, ["License :: OSI Approved :: BSD License"]),
+        # "v3" does not say -only or -or-later, like the GPLv3 classifier
+        (
+            None,
+            None,
+            ["License :: OSI Approved :: GNU Affero General Public License v3"],
+        ),
         # classifiers with no entry that maps to SPDX (see issue #1372)
         (None, None, ["Programming Language :: Python :: 3"]),
         (None, None, ["License :: OSI Approved"]),