diff --git a/swh/storage/migrate_extrinsic_metadata.py b/swh/storage/migrate_extrinsic_metadata.py
--- a/swh/storage/migrate_extrinsic_metadata.py
+++ b/swh/storage/migrate_extrinsic_metadata.py
@@ -127,6 +127,29 @@
         return filename.split("-")[0]
     elif filename.startswith("devpi-theme-16-"):
         return "devpi-theme-16"
+    elif re.match("[^-]+-[0-9]+.tar.gz", filename):
+        return filename.split("-")[0]
+    elif filename == "ohai-1!0.tar.gz":
+        return "ohai"
+    elif filename == "collective.topicitemsevent-0.1dvl.tar.gz":
+        return "collective.topicitemsevent"
+    elif filename.startswith(
+        ("SpiNNStorageHandlers-1!", "sPyNNakerExternalDevicesPlugin-1!")
+    ):
+        return filename.split("-")[0]
+    elif filename.startswith("limnoria-201"):
+        return "limnoria"
+    elif filename.startswith("pytz-20"):
+        return "pytz"
+    elif filename.startswith("youtube_dl_server-alpha."):
+        return "youtube_dl_server"
+    elif filename == "json-extensions-b76bc7d.tar.gz":
+        return "json-extensions"
+    elif filename == "LitReview-0.6989ev.tar.gz":
+        # typo of "dev"
+        return "LitReview"
+    elif filename.startswith("django_options-r"):
+        return "django_options"
     filename = filename.replace(" ", "-")
 
     match = re.match(
@@ -138,13 +161,38 @@
     if match:
         return match.group("project_name")
 
+    # First try with a rather strict format, but that allows accidentally
+    # matching the version as part of the package name
     match = re.match(
-        r"^(?P<project_name>[a-z0-9_.]+(-[a-z0-9_.]*[a-z][a-z0-9_.]*)*)"  # project name
-        r"-v?[0-9_.]+([a-z]+[0-9]+)?(dev|pre|[a-c])?"  # "main" version
-        r"(\.post[0-9]*)?"  # suffix generated by vcversioner/setuptools-scm/...
+        r"^(?P<project_name>[a-z0-9_.]+?([-_][a-z][a-z0-9.]+?)*?)"  # project name
+        r"-v?"
+        r"([0-9]+!)?"  # epoch
+        r"[0-9_.]+([a-z]+[0-9]+)?"  # "main" version
         r"([.-]?(alpha|beta|dev|post|pre|rc)(\.?[0-9]+)?)*"  # development status
+        r"([.-]?20[012][0-9]{5,9})?"  # date
         r"([.-]g?[0-9a-f]+)?"  # git commit
-        r"(-[a-z][a-z0-9]*)?"  # extra suffixes
+        r"(-py(thon)?[23](\.?[0-9]{1,2})?)?"  # python version
+        r"\.(tar\.gz|tar\.bz2|tgz|zip)$",  # extension
+        filename,
+        re.I,
+    )
+    if match:
+        return match.group("project_name")
+
+    # If that doesn't work, give up on trying to parse version suffixes,
+    # and just find the first version-like occurrence in the file name
+
+    match = re.match(
+        r"^(?P<project_name>[a-z0-9_.-]+?)"  # project name
+        r"[-_.]v?"
+        r"([0-9]+!)?"  # epoch
+        r"("  # "main" version
+        r"[0-9_]+\.[0-9_.]+([a-z]+[0-9]+)?"  # classic version number
+        r"|20[012][0-9]{5,9}"  # date as integer
+        r"|20[012][0-9]-[01][0-9]-[0-3][0-9]"  # date as ISO 8601
+        r")"  # end of "main" version
+        r"[a-z]?(dev|pre)?"  # direct version suffix
+        r"([._-].*)?"  # extra suffixes
         r"\.(tar\.gz|tar\.bz2|tgz|zip)$",  # extension
         filename,
         re.I,
diff --git a/swh/storage/tests/migrate_extrinsic_metadata/test_pypi.py b/swh/storage/tests/migrate_extrinsic_metadata/test_pypi.py
--- a/swh/storage/tests/migrate_extrinsic_metadata/test_pypi.py
+++ b/swh/storage/tests/migrate_extrinsic_metadata/test_pypi.py
@@ -85,6 +85,35 @@
         ("obedient.powny-3.0.0-alpha-20141027-2102-9e53ebd.tar.gz", "obedient.powny"),
         ("mojimoji-0.0.9_2.tar.gz", "mojimoji"),
         ("devpi-theme-16-2.0.0.tar.gz", "devpi-theme-16"),
+        ("Orange3-WONDER-1-1.0.7.tar.gz", "Orange3-WONDER-1"),
+        ("obj-34.tar.gz", "obj"),
+        ("pytorch-ignite-nightly-20190825.tar.gz", "pytorch-ignite-nightly"),
+        ("tlds-2019081900.tar.gz", "tlds"),
+        ("dominator-12.1.2-alpha-20141027-1446-ad46e0f.tar.gz", "dominator"),
+        ("waferslim-1.0.0-py3.1.zip", "waferslim"),
+        ("Beaver-21.tar.gz", "Beaver"),
+        ("aimmo-0.post.dev460.tar.gz", "aimmo"),
+        ("ohai-1!0.tar.gz", "ohai"),
+        ("nevolution-risk-139.tar.gz", "nevolution-risk"),
+        ("collective.topicitemsevent-0.1dvl.tar.gz", "collective.topicitemsevent"),
+        ("lesscpy-0.9g.tar.gz", "lesscpy"),
+        ("SpiNNStorageHandlers-1!4.0.0a1.tar.gz", "SpiNNStorageHandlers"),
+        ("limnoria-2013-03-27T16:32:26+0100.tar.gz", "limnoria"),
+        (
+            "sPyNNakerExternalDevicesPlugin-1!4.0.0a2.tar.gz",
+            "sPyNNakerExternalDevicesPlugin",
+        ),
+        ("django-bootstrap-italia_0.1.tar.gz", "django-bootstrap-italia"),
+        ("sPyNNaker8-1!4.0.0a1.tar.gz", "sPyNNaker8"),
+        ("betahaus.openmember-0.1adev-r1651.tar.gz", "betahaus.openmember"),
+        ("mailer.0.8.0.zip", "mailer"),
+        ("pytz-2005k.tar.bz2", "pytz"),
+        ("aha.plugin.microne-0.62bdev.tar.gz", "aha.plugin.microne"),
+        ("youtube_dl_server-alpha.3.tar.gz", "youtube_dl_server"),
+        ("json-extensions-b76bc7d.tar.gz", "json-extensions"),
+        ("LitReview-0.6989ev.tar.gz", "LitReview"),
+        ("django_options-r5.tar.gz", "django_options"),
+        ("ddlib-2013-11-07.tar.gz", "ddlib"),
     ]
 
     for (filename, project) in files: