diff --git a/swh/loader/pypi/loader.py b/swh/loader/pypi/loader.py
--- a/swh/loader/pypi/loader.py
+++ b/swh/loader/pypi/loader.py
@@ -236,10 +236,19 @@
     def generate_and_load_snapshot(self):
         branches = {}
         for release, artifacts in self.project.all_release_artifacts().items():
-            for filename, sha256 in artifacts:
-                branch_name = filename
+            if len(artifacts) == 1:
+                # Only one artifact for this release, generate a single branch
+                branch_name = 'refs/tags/%s' % release
+                filename, sha256 = artifacts[0]
                 target = self.target_from_artifact(filename, sha256)
                 branches[branch_name.encode('utf-8')] = target
+            else:
+                # Several artifacts for this release, generate a separate
+                # pointer for each of them
+                for filename, sha256 in artifacts:
+                    branch_name = 'refs/tags/%s/%s' % (release, filename)
+                    target = self.target_from_artifact(filename, sha256)
+                    branches[branch_name.encode('utf-8')] = target
 
         snapshot = {
             'branches': branches,
diff --git a/swh/loader/pypi/tests/test_loader.py b/swh/loader/pypi/tests/test_loader.py
--- a/swh/loader/pypi/tests/test_loader.py
+++ b/swh/loader/pypi/tests/test_loader.py
@@ -189,17 +189,17 @@
         self.assertRevisionsOk(expected_revisions)
 
         expected_branches = {
-            '0805nexter-1.1.0.zip': {
+            'refs/tags/1.1.0': {
                 'target': '4c99891f93b81450385777235a37b5e966dd1571',
                 'target_type': 'revision',
             },
-            '0805nexter-1.2.0.zip': {
+            'refs/tags/1.2.0': {
                 'target': 'e445da4da22b31bfebb6ffc4383dbf839a074d21',
                 'target_type': 'revision',
             },
         }
 
-        self.assertSnapshotOk('f456b03e8bf1920d64b00df234b1efedc25b6c93',
+        self.assertSnapshotOk('c111b9a5f46e68e5017b04383281cfd932ab3fb8',
                               expected_branches)
 
 
@@ -211,14 +211,14 @@
     def _last_snapshot(self):
         """Return last visited snapshot"""
         return {
-            'id': b'\xf4V\xb0>\x8b\xf1\x92\rd\xb0\r\xf24\xb1\xef\xed\xc2[l\x93',  # noqa
+            'id': b'\xc1\x11\xb9\xa5\xf4nh\xe5\x01{\x0482\x81\xcf\xd92\xab?\xb8',  # noqa
             'branches': {
-                b'0805nexter-1.1.0.zip': {
+                b'refs/tags/1.1.0': {
                     'target': b'L\x99\x89\x1f\x93\xb8\x14P'
                     b'8Ww#Z7\xb5\xe9f\xdd\x15q',
                     'target_type': 'revision'
                 },
-                b'0805nexter-1.2.0.zip': {
+                b'refs/tags/1.2.0': {
                     'target': b'\xe4E\xdaM\xa2+1\xbf'
                     b'\xeb\xb6\xff\xc48=\xbf\x83'
                     b'\x9a\x07M!',
@@ -273,13 +273,13 @@
         self.assertDirectoriesOk([])
         self.assertRevisionsOk(expected_revisions={})
 
-        expected_snapshot_id = 'f456b03e8bf1920d64b00df234b1efedc25b6c93'
+        expected_snapshot_id = 'c111b9a5f46e68e5017b04383281cfd932ab3fb8'
         expected_branches = {
-            '0805nexter-1.1.0.zip': {
+            'refs/tags/1.1.0': {
                 'target': '4c99891f93b81450385777235a37b5e966dd1571',
                 'target_type': 'revision',
             },
-            '0805nexter-1.2.0.zip': {
+            'refs/tags/1.2.0': {
                 'target': 'e445da4da22b31bfebb6ffc4383dbf839a074d21',
                 'target_type': 'revision',
             },
@@ -358,17 +358,17 @@
         for rev, dir_id in old_revisions.items():
             expected_revisions[rev] = dir_id
 
-        expected_snapshot_id = 'e5beda90e9ddbc8672734ed172246b06fcbc6827'
+        expected_snapshot_id = '78fe3367ba98ed8b679b91ca70d3f68130fa0694'
         expected_branches = {
-            '0805nexter-1.1.0.zip': {
+            'refs/tags/1.1.0': {
                 'target': '4c99891f93b81450385777235a37b5e966dd1571',
                 'target_type': 'revision',
             },
-            '0805nexter-1.2.0.zip': {
+            'refs/tags/1.2.0': {
                 'target': 'e445da4da22b31bfebb6ffc4383dbf839a074d21',
                 'target_type': 'revision',
             },
-            '0805nexter-1.3.0.zip': {
+            'refs/tags/1.3.0': {
                 'target': 'fb46e49605b0bbe69f8c53d315e89370e7c6cb5d',
                 'target_type': 'revision',
             },
@@ -388,17 +388,17 @@
     def _last_snapshot(self):
         """Return last visited snapshot"""
         return {
-            'id': b"\xe5\xbe\xda\x90\xe9\xdd\xbc\x86rsN\xd1r$k\x06\xfc\xbch'",
+            'id': b'x\xfe3g\xba\x98\xed\x8bg\x9b\x91\xcap\xd3\xf6\x810\xfa\x06\x94',  # noqa
             'branches': {
-                b'0805nexter-1.1.0.zip': {
+                b'refs/tags/1.1.0': {
                     'target': b'L\x99\x89\x1f\x93\xb8\x14P8Ww#Z7\xb5\xe9f\xdd\x15q',  # noqa
                     'target_type': 'revision'
                 },
-                b'0805nexter-1.2.0.zip': {
+                b'refs/tags/1.2.0': {
                     'target': b'\xe4E\xdaM\xa2+1\xbf\xeb\xb6\xff\xc48=\xbf\x83\x9a\x07M!',  # noqa
                     'target_type': 'revision'
                 },
-                b'0805nexter-1.3.0.zip': {
+                b'refs/tags/1.3.0': {
                     'target': b'\xfbF\xe4\x96\x05\xb0\xbb\xe6\x9f\x8cS\xd3\x15\xe8\x93p\xe7\xc6\xcb]',  # noqa
                     'target_type': 'revision'
                 }
@@ -487,17 +487,17 @@
         }
         self.assertRevisionsOk(expected_revisions)
 
-        expected_snapshot_id = 'fb192f35397812776377fa758e0ba4cf20a4cf5d'
+        expected_snapshot_id = '388083a9bb675812c6cc7124e1f8af8128df6917'
         expected_branches = {
-            '0805nexter-1.2.0.zip': {
+            'refs/tags/1.2.0': {
                 'target': 'e445da4da22b31bfebb6ffc4383dbf839a074d21',
                 'target_type': 'revision',
             },
-            '0805nexter-1.3.0.zip': {
+            'refs/tags/1.3.0': {
                 'target': 'fb46e49605b0bbe69f8c53d315e89370e7c6cb5d',
                 'target_type': 'revision',
             },
-            '0805nexter-1.4.0.zip': {
+            'refs/tags/1.4.0': {
                 'target': '5e91875f096ac48c98d74acf307439a3490f2827',
                 'target_type': 'revision',
             },