diff --git a/docs/new_lister_template.py b/docs/new_lister_template.py
--- a/docs/new_lister_template.py
+++ b/docs/new_lister_template.py
@@ -11,7 +11,7 @@
 import requests
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -77,11 +77,11 @@
     def state_to_dict(self, state: NewForgeListerState) -> Dict[str, Any]:
         return asdict(state)
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(self, url, params) -> requests.Response:
         # Do the network resource request under a retrying decorator
         # to handle rate limiting and transient errors up to a limit.
-        # `throttling_retry` by default use the `requests` library to check
+        # `http_retry` by default use the `requests` library to check
         # only for rate-limit and a base-10 exponential waiting strategy.
         # This can be customized by passed waiting, retrying and logging strategies
         # as functions. See the `tenacity` library documentation.
diff --git a/docs/tutorial.rst b/docs/tutorial.rst
--- a/docs/tutorial.rst
+++ b/docs/tutorial.rst
@@ -317,7 +317,7 @@
 then immediately stop the listing by doing an equivalent of
 :py:meth:`Response.raise_for_status` from the ``requests`` library. As for rate-limiting
 errors, we have a strategy of using a flexible decorator to handle the retrying for us.
-It is based on the ``tenacity`` library and accessible as :py:func:`throttling_retry` from
+It is based on the ``tenacity`` library and accessible as :py:func:`http_retry` from
 :py:mod:`swh.lister.utils`.
 
 Pagination
diff --git a/swh/lister/arch/lister.py b/swh/lister/arch/lister.py
--- a/swh/lister/arch/lister.py
+++ b/swh/lister/arch/lister.py
@@ -16,7 +16,7 @@
 import requests
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.model.hashutil import hash_to_hex
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
@@ -132,7 +132,7 @@
             }
         )
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def request_get(self, url: str, params: Dict[str, Any]) -> requests.Response:
 
         logger.debug("Fetching URL %s with params %s", url, params)
diff --git a/swh/lister/bitbucket/lister.py b/swh/lister/bitbucket/lister.py
--- a/swh/lister/bitbucket/lister.py
+++ b/swh/lister/bitbucket/lister.py
@@ -14,7 +14,7 @@
 import requests
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -107,7 +107,7 @@
         if username is not None and password is not None:
             self.session.auth = (username, password)
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.DEBUG))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.DEBUG))
     def page_request(self, last_repo_cdate: str) -> requests.Response:
 
         self.url_params["after"] = last_repo_cdate
diff --git a/swh/lister/bower/lister.py b/swh/lister/bower/lister.py
--- a/swh/lister/bower/lister.py
+++ b/swh/lister/bower/lister.py
@@ -8,7 +8,7 @@
 import requests
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -49,7 +49,7 @@
             }
         )
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(self, url: str, params: Dict[str, Any]) -> requests.Response:
 
         logger.info("Fetching URL %s with params %s", url, params)
diff --git a/swh/lister/cgit/lister.py b/swh/lister/cgit/lister.py
--- a/swh/lister/cgit/lister.py
+++ b/swh/lister/cgit/lister.py
@@ -15,7 +15,7 @@
 
 from swh.lister import USER_AGENT
 from swh.lister.pattern import CredentialsType, StatelessLister
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -79,7 +79,7 @@
         )
         self.base_git_url = base_git_url
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.DEBUG))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.DEBUG))
     def _get_and_parse(self, url: str) -> BeautifulSoup:
         """Get the given url and parse the retrieved HTML using BeautifulSoup"""
         response = self.session.get(url)
diff --git a/swh/lister/gitea/tests/test_lister.py b/swh/lister/gitea/tests/test_lister.py
--- a/swh/lister/gitea/tests/test_lister.py
+++ b/swh/lister/gitea/tests/test_lister.py
@@ -138,7 +138,7 @@
     assert stats.pages == 1
 
 
-@pytest.mark.parametrize("http_code", [400, 500, 502])
+@pytest.mark.parametrize("http_code", [400, 500])
 def test_gitea_list_http_error(
     swh_scheduler, requests_mock, http_code, trygitea_p1, trygitea_p2
 ):
diff --git a/swh/lister/gitlab/lister.py b/swh/lister/gitlab/lister.py
--- a/swh/lister/gitlab/lister.py
+++ b/swh/lister/gitlab/lister.py
@@ -17,7 +17,7 @@
 
 from swh.lister import USER_AGENT
 from swh.lister.pattern import CredentialsType, Lister
-from swh.lister.utils import is_retryable_exception, throttling_retry
+from swh.lister.utils import http_retry, is_retryable_exception
 from swh.scheduler.model import ListedOrigin
 
 logger = logging.getLogger(__name__)
@@ -138,7 +138,7 @@
     def state_to_dict(self, state: GitLabListerState) -> Dict[str, Any]:
         return asdict(state)
 
-    @throttling_retry(
+    @http_retry(
         retry=_if_rate_limited, before_sleep=before_sleep_log(logger, logging.WARNING)
     )
     def get_page_result(self, url: str) -> PageResult:
diff --git a/swh/lister/gogs/lister.py b/swh/lister/gogs/lister.py
--- a/swh/lister/gogs/lister.py
+++ b/swh/lister/gogs/lister.py
@@ -12,7 +12,7 @@
 import requests
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -116,7 +116,7 @@
     def state_to_dict(self, state: GogsListerState) -> Dict[str, Any]:
         return asdict(state)
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(
         self, url: str, params: Dict[str, Any]
     ) -> Tuple[Dict[str, Any], Dict[str, Any]]:
diff --git a/swh/lister/gogs/tests/test_lister.py b/swh/lister/gogs/tests/test_lister.py
--- a/swh/lister/gogs/tests/test_lister.py
+++ b/swh/lister/gogs/tests/test_lister.py
@@ -177,7 +177,7 @@
     assert stats.origins == 6
 
 
-@pytest.mark.parametrize("http_code", [400, 500, 502])
+@pytest.mark.parametrize("http_code", [400, 500])
 def test_gogs_list_http_error(
     swh_scheduler, requests_mock, http_code, trygogs_p1, trygogs_p3_last
 ):
diff --git a/swh/lister/golang/lister.py b/swh/lister/golang/lister.py
--- a/swh/lister/golang/lister.py
+++ b/swh/lister/golang/lister.py
@@ -13,7 +13,7 @@
 import requests
 from tenacity import before_sleep_log
 
-from swh.lister.utils import retry_policy_generic, throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -87,8 +87,7 @@
             ):
                 self.updated = True
 
-    @throttling_retry(
-        retry=retry_policy_generic,
+    @http_retry(
         before_sleep=before_sleep_log(logger, logging.WARNING),
     )
     def api_request(self, url: str) -> List[str]:
diff --git a/swh/lister/launchpad/lister.py b/swh/lister/launchpad/lister.py
--- a/swh/lister/launchpad/lister.py
+++ b/swh/lister/launchpad/lister.py
@@ -14,7 +14,7 @@
 from lazr.restfulclient.resource import Collection
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import retry_if_exception, throttling_retry
+from swh.lister.utils import http_retry, retry_if_exception
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -100,7 +100,7 @@
                     d[attribute_name] = date_last_modified.isoformat()
         return d
 
-    @throttling_retry(
+    @http_retry(
         retry=retry_if_restful_error,
         before_sleep=before_sleep_log(logger, logging.WARNING),
     )
diff --git a/swh/lister/maven/lister.py b/swh/lister/maven/lister.py
--- a/swh/lister/maven/lister.py
+++ b/swh/lister/maven/lister.py
@@ -16,7 +16,7 @@
 from tenacity.before_sleep import before_sleep_log
 
 from swh.core.github.utils import GitHubSession
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -112,7 +112,7 @@
     def state_to_dict(self, state: MavenListerState) -> Dict[str, Any]:
         return asdict(state)
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(self, url: str, params: Dict[str, Any]) -> requests.Response:
 
         logger.info("Fetching URL %s with params %s", url, params)
diff --git a/swh/lister/maven/tests/test_lister.py b/swh/lister/maven/tests/test_lister.py
--- a/swh/lister/maven/tests/test_lister.py
+++ b/swh/lister/maven/tests/test_lister.py
@@ -125,6 +125,11 @@
     requests_mock.get(URL_POM_3, content=maven_pom_3)
 
 
+@pytest.fixture(autouse=True)
+def retry_sleep_mock(mocker):
+    mocker.patch.object(MavenLister.page_request.retry, "sleep")
+
+
 def test_maven_full_listing(swh_scheduler):
     """Covers full listing of multiple pages, checking page results and listed
     origins, statelessness."""
diff --git a/swh/lister/npm/lister.py b/swh/lister/npm/lister.py
--- a/swh/lister/npm/lister.py
+++ b/swh/lister/npm/lister.py
@@ -12,7 +12,7 @@
 
 from swh.lister import USER_AGENT
 from swh.lister.pattern import CredentialsType, Lister
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -95,7 +95,7 @@
             params["startkey"] = last_package_id
         return params
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(self, last_package_id: str) -> requests.Response:
         params = self.request_params(last_package_id)
         logger.debug("Fetching URL %s with params %s", self.url, params)
diff --git a/swh/lister/npm/tests/test_lister.py b/swh/lister/npm/tests/test_lister.py
--- a/swh/lister/npm/tests/test_lister.py
+++ b/swh/lister/npm/tests/test_lister.py
@@ -35,6 +35,11 @@
     return json.loads(Path(datadir, "npm_incremental_page2.json").read_text())
 
 
+@pytest.fixture(autouse=True)
+def retry_sleep_mock(mocker):
+    mocker.patch.object(NpmLister.page_request.retry, "sleep")
+
+
 def _check_listed_npm_packages(lister, packages, scheduler_origins):
     for package in packages:
         package_name = package["doc"]["name"]
diff --git a/swh/lister/pubdev/lister.py b/swh/lister/pubdev/lister.py
--- a/swh/lister/pubdev/lister.py
+++ b/swh/lister/pubdev/lister.py
@@ -10,7 +10,7 @@
 from requests.exceptions import HTTPError
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -60,7 +60,7 @@
             }
         )
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(self, url: str, params: Dict[str, Any]) -> requests.Response:
 
         logger.debug("Fetching URL %s with params %s", url, params)
diff --git a/swh/lister/pypi/lister.py b/swh/lister/pypi/lister.py
--- a/swh/lister/pypi/lister.py
+++ b/swh/lister/pypi/lister.py
@@ -13,7 +13,7 @@
 
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -88,7 +88,7 @@
     def state_to_dict(self, state: PyPIListerState) -> Dict[str, Any]:
         return asdict(state)
 
-    @throttling_retry(
+    @http_retry(
         retry=_if_rate_limited, before_sleep=before_sleep_log(logger, logging.WARNING)
     )
     def _changelog_last_serial(self, client: ServerProxy) -> int:
@@ -97,7 +97,7 @@
         assert isinstance(serial, int)
         return serial
 
-    @throttling_retry(
+    @http_retry(
         retry=_if_rate_limited, before_sleep=before_sleep_log(logger, logging.WARNING)
     )
     def _changelog_since_serial(
diff --git a/swh/lister/sourceforge/lister.py b/swh/lister/sourceforge/lister.py
--- a/swh/lister/sourceforge/lister.py
+++ b/swh/lister/sourceforge/lister.py
@@ -18,7 +18,7 @@
 from tenacity.before_sleep import before_sleep_log
 
 from swh.core.api.classes import stream_results
-from swh.lister.utils import retry_policy_generic, throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -208,8 +208,7 @@
         self._project_last_modified = listed_origins
         return listed_origins
 
-    @throttling_retry(
-        retry=retry_policy_generic,
+    @http_retry(
         before_sleep=before_sleep_log(logger, logging.WARNING),
     )
     def page_request(self, url, params) -> requests.Response:
diff --git a/swh/lister/tests/test_utils.py b/swh/lister/tests/test_utils.py
--- a/swh/lister/tests/test_utils.py
+++ b/swh/lister/tests/test_utils.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2018-2021 the Software Heritage developers
+# Copyright (C) 2018-2022 the Software Heritage developers
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
@@ -7,12 +7,7 @@
 from requests.status_codes import codes
 from tenacity.wait import wait_fixed
 
-from swh.lister.utils import (
-    MAX_NUMBER_ATTEMPTS,
-    WAIT_EXP_BASE,
-    split_range,
-    throttling_retry,
-)
+from swh.lister.utils import MAX_NUMBER_ATTEMPTS, WAIT_EXP_BASE, http_retry, split_range
 
 
 @pytest.mark.parametrize(
@@ -51,7 +46,7 @@
 TEST_URL = "https://example.og/api/repositories"
 
 
-@throttling_retry()
+@http_retry()
 def make_request():
     response = requests.get(TEST_URL)
     response.raise_for_status()
@@ -62,13 +57,22 @@
     mock_sleep.assert_has_calls([mocker.call(param) for param in sleep_params])
 
 
-def test_throttling_retry(requests_mock, mocker):
+@pytest.mark.parametrize(
+    "status_code",
+    [
+        codes.too_many_requests,
+        codes.internal_server_error,
+        codes.bad_gateway,
+        codes.service_unavailable,
+    ],
+)
+def test_http_retry(requests_mock, mocker, status_code):
     data = {"result": {}}
     requests_mock.get(
         TEST_URL,
         [
-            {"status_code": codes.too_many_requests},
-            {"status_code": codes.too_many_requests},
+            {"status_code": status_code},
+            {"status_code": status_code},
             {"status_code": codes.ok, "json": data},
         ],
     )
@@ -82,7 +86,7 @@
     assert response.json() == data
 
 
-def test_throttling_retry_max_attemps(requests_mock, mocker):
+def test_http_retry_max_attemps(requests_mock, mocker):
     requests_mock.get(
         TEST_URL,
         [{"status_code": codes.too_many_requests}] * (MAX_NUMBER_ATTEMPTS),
@@ -102,14 +106,14 @@
     )
 
 
-@throttling_retry(wait=wait_fixed(WAIT_EXP_BASE))
+@http_retry(wait=wait_fixed(WAIT_EXP_BASE))
 def make_request_wait_fixed():
     response = requests.get(TEST_URL)
     response.raise_for_status()
     return response
 
 
-def test_throttling_retry_wait_fixed(requests_mock, mocker):
+def test_http_retry_wait_fixed(requests_mock, mocker):
     requests_mock.get(
         TEST_URL,
         [
diff --git a/swh/lister/tuleap/lister.py b/swh/lister/tuleap/lister.py
--- a/swh/lister/tuleap/lister.py
+++ b/swh/lister/tuleap/lister.py
@@ -11,7 +11,7 @@
 import requests
 from tenacity.before_sleep import before_sleep_log
 
-from swh.lister.utils import throttling_retry
+from swh.lister.utils import http_retry
 from swh.scheduler.interface import SchedulerInterface
 from swh.scheduler.model import ListedOrigin
 
@@ -65,7 +65,7 @@
             }
         )
 
-    @throttling_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
+    @http_retry(before_sleep=before_sleep_log(logger, logging.WARNING))
     def page_request(self, url: str, params: Dict[str, Any]) -> requests.Response:
 
         logger.info("Fetching URL %s with params %s", url, params)
diff --git a/swh/lister/tuleap/tests/test_lister.py b/swh/lister/tuleap/tests/test_lister.py
--- a/swh/lister/tuleap/tests/test_lister.py
+++ b/swh/lister/tuleap/tests/test_lister.py
@@ -92,6 +92,11 @@
     return text, headers, page_results, origin_urls
 
 
+@pytest.fixture(autouse=True)
+def retry_sleep_mock(mocker):
+    mocker.patch.object(TuleapLister.page_request.retry, "sleep")
+
+
 def check_listed_origins(lister_urls: List[str], scheduler_origins: List[ListedOrigin]):
     """Asserts that the two collections have the same origin URLs.
 
diff --git a/swh/lister/utils.py b/swh/lister/utils.py
--- a/swh/lister/utils.py
+++ b/swh/lister/utils.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2018-2021 the Software Heritage developers
+# Copyright (C) 2018-2022 the Software Heritage developers
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
@@ -66,14 +66,6 @@
     return False
 
 
-def retry_if_throttling(retry_state) -> bool:
-    """
-    Custom tenacity retry predicate for handling HTTP responses with
-    status code 429 (too many requests).
-    """
-    return retry_if_exception(retry_state, is_throttling_exception)
-
-
 def retry_policy_generic(retry_state) -> bool:
     """
     Custom tenacity retry predicate for handling failed requests:
@@ -90,8 +82,8 @@
 MAX_NUMBER_ATTEMPTS = 5
 
 
-def throttling_retry(
-    retry=retry_if_throttling,
+def http_retry(
+    retry=retry_policy_generic,
     wait=wait_exponential(exp_base=WAIT_EXP_BASE),
     stop=stop_after_attempt(max_attempt_number=MAX_NUMBER_ATTEMPTS),
     **retry_args,