diff --git a/swh/deposit/tests/api/test_deposit_list.py b/swh/deposit/tests/api/test_deposit_private_list.py
similarity index 91%
rename from swh/deposit/tests/api/test_deposit_list.py
rename to swh/deposit/tests/api/test_deposit_private_list.py
index 013a6493..505da6ae 100644
--- a/swh/deposit/tests/api/test_deposit_list.py
+++ b/swh/deposit/tests/api/test_deposit_private_list.py
@@ -1,100 +1,97 @@
 # Copyright (C) 2017-2021  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
 from django.urls import reverse_lazy as reverse
 from rest_framework import status
 
 from swh.deposit.api.converters import convert_status_detail
 from swh.deposit.config import (
     DEPOSIT_STATUS_DEPOSITED,
     DEPOSIT_STATUS_PARTIAL,
     PRIVATE_LIST_DEPOSITS,
 )
 
 STATUS_DETAIL = {
     "url": {
         "summary": "At least one compatible url field. Failed",
         "fields": ["testurl"],
     },
     "metadata": [{"summary": "Mandatory fields missing", "fields": ["9", 10, 1.212],},],
     "archive": [
         {"summary": "Invalid archive", "fields": ["3"],},
         {"summary": "Unsupported archive", "fields": [2],},
     ],
 }
 
 
 def test_deposit_list(partial_deposit, deposited_deposit, authenticated_client):
     """Deposit list api should return all deposits in a paginated way
 
     """
     partial_deposit.status_detail = STATUS_DETAIL
     partial_deposit.save()
 
     deposit_id = partial_deposit.id
     deposit_id2 = deposited_deposit.id
 
-    # NOTE: does not work as documented
-    # https://docs.djangoproject.com/en/1.11/ref/urlresolvers/#django.core.urlresolvers.reverse  # noqa
-    # url = reverse(PRIVATE_LIST_DEPOSITS, kwargs={'page_size': 1})
     main_url = reverse(PRIVATE_LIST_DEPOSITS)
     url = "%s?page_size=1" % main_url
     response = authenticated_client.get(url)
 
     assert response.status_code == status.HTTP_200_OK
     data = response.json()
-    assert data["count"] == 2  # 2 deposits
+    assert data["count"] == 2  # total result of 2 deposits if consuming all results
     expected_next = f"{main_url}?page=2&page_size=1"
     assert data["next"].endswith(expected_next) is True
     assert data["previous"] is None
     assert len(data["results"]) == 1  # page of size 1
     deposit = data["results"][0]
     assert deposit["id"] == deposit_id
     assert deposit["status"] == DEPOSIT_STATUS_PARTIAL
     expected_status_detail = convert_status_detail(STATUS_DETAIL)
     assert deposit["status_detail"] == expected_status_detail
 
     # then 2nd page
     response2 = authenticated_client.get(expected_next)
 
     assert response2.status_code == status.HTTP_200_OK
     data2 = response2.json()
 
-    assert data2["count"] == 2  # still 2 deposits
+    assert data["count"] == 2  # total result of 2 deposits if consuming all results
     assert data2["next"] is None
 
     expected_previous = f"{main_url}?page_size=1"
     assert data2["previous"].endswith(expected_previous) is True
     assert len(data2["results"]) == 1  # page of size 1
 
     deposit2 = data2["results"][0]
     assert deposit2["id"] == deposit_id2
     assert deposit2["status"] == DEPOSIT_STATUS_DEPOSITED
 
 
 def test_deposit_list_exclude(partial_deposit, deposited_deposit, authenticated_client):
     """Exclusion pattern on external_id should be respected
 
     """
     partial_deposit.status_detail = STATUS_DETAIL
     partial_deposit.save()
 
     main_url = reverse(PRIVATE_LIST_DEPOSITS)
 
     # Testing exclusion pattern
     exclude_pattern = "external-id"
     assert partial_deposit.external_id.startswith(exclude_pattern)
     assert deposited_deposit.external_id.startswith(exclude_pattern)
     url = f"{main_url}?page_size=1&exclude=external-id"
     response = authenticated_client.get(url)
     assert response.status_code == status.HTTP_200_OK
     data = response.json()
     assert data["count"] == 0
 
     url = "%s?page_size=1&exclude=dummy" % main_url  # that won't exclude anything
     response = authenticated_client.get(url)
     assert response.status_code == status.HTTP_200_OK
     data = response.json()
     assert data["count"] == 2