diff --git a/swh/core/api/gunicorn_config.py b/swh/core/api/gunicorn_config.py
--- a/swh/core/api/gunicorn_config.py
+++ b/swh/core/api/gunicorn_config.py
@@ -22,6 +22,7 @@
     default_sentry_dsn=None,
     flask=True,
     sentry_integrations=None,
+    ignored_exceptions=(),
     extra_sentry_kwargs={},
 ):
     # Initializes sentry as soon as possible in gunicorn's worker processes.
@@ -36,4 +37,5 @@
         default_sentry_dsn,
         integrations=sentry_integrations,
         extra_kwargs=extra_sentry_kwargs,
+        ignored_exceptions=ignored_exceptions,
     )
diff --git a/swh/core/api/tests/test_gunicorn.py b/swh/core/api/tests/test_gunicorn.py
--- a/swh/core/api/tests/test_gunicorn.py
+++ b/swh/core/api/tests/test_gunicorn.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2019  The Software Heritage developers
+# Copyright (C) 2019-2022  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
@@ -27,12 +27,17 @@
             with patch.dict(os.environ, {"SWH_SENTRY_DSN": "test_dsn"}):
                 gunicorn_config.post_fork(None, None)
 
+    # before_send is obtained from functools.partial, and we cannot compare these
+    # with equality
+    before_send = sentry_sdk_init.call_args[1]["before_send"]
+
     sentry_sdk_init.assert_called_once_with(
         dsn="test_dsn",
         integrations=[flask_integration],
         debug=False,
         release=None,
         environment=None,
+        before_send=before_send,
     )
 
 
@@ -54,12 +59,17 @@
 
     version = pkg_resources.get_distribution("swh.core").version
 
+    # before_send is obtained from functools.partial, and we cannot compare these
+    # with equality
+    before_send = sentry_sdk_init.call_args[1]["before_send"]
+
     sentry_sdk_init.assert_called_once_with(
         dsn="test_dsn",
         integrations=[flask_integration],
         debug=False,
         release="swh.core@" + version,
         environment="tests",
+        before_send=before_send,
     )
 
 
@@ -74,12 +84,17 @@
             ):
                 gunicorn_config.post_fork(None, None)
 
+    # before_send is obtained from functools.partial, and we cannot compare these
+    # with equality
+    before_send = sentry_sdk_init.call_args[1]["before_send"]
+
     sentry_sdk_init.assert_called_once_with(
         dsn="test_dsn",
         integrations=[flask_integration],
         debug=True,
         release=None,
         environment=None,
+        before_send=before_send,
     )
 
 
@@ -88,12 +103,17 @@
         with patch.dict(os.environ, {"SWH_SENTRY_DSN": "test_dsn"}):
             gunicorn_config.post_fork(None, None, flask=False)
 
+    # before_send is obtained from functools.partial, and we cannot compare these
+    # with equality
+    before_send = sentry_sdk_init.call_args[1]["before_send"]
+
     sentry_sdk_init.assert_called_once_with(
         dsn="test_dsn",
         integrations=[],
         debug=False,
         release=None,
         environment=None,
+        before_send=before_send,
     )
 
 
@@ -111,6 +131,10 @@
                     extra_sentry_kwargs={"bar": "baz"},
                 )
 
+    # before_send is obtained from functools.partial, and we cannot compare these
+    # with equality
+    before_send = sentry_sdk_init.call_args[1]["before_send"]
+
     sentry_sdk_init.assert_called_once_with(
         dsn="test_dsn",
         integrations=["foo", flask_integration],
@@ -118,4 +142,5 @@
         bar="baz",
         release=None,
         environment=None,
+        before_send=before_send,
     )
diff --git a/swh/core/sentry.py b/swh/core/sentry.py
--- a/swh/core/sentry.py
+++ b/swh/core/sentry.py
@@ -3,6 +3,7 @@
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
+import functools
 import os
 
 import pkg_resources
@@ -17,7 +18,17 @@
         return None
 
 
-def init_sentry(sentry_dsn, *, debug=None, integrations=[], extra_kwargs={}):
+def before_send(ignored_exceptions, event, hint):
+    if "exc_info" in hint:
+        exc_type, exc_value, tb = hint["exc_info"]
+        if isinstance(exc_value, ignored_exceptions):
+            return None
+    return event
+
+
+def init_sentry(
+    sentry_dsn, *, debug=None, integrations=[], ignored_exceptions=(), extra_kwargs={}
+):
     if debug is None:
         debug = bool(os.environ.get("SWH_SENTRY_DEBUG"))
     sentry_dsn = sentry_dsn or os.environ.get("SWH_SENTRY_DSN")
@@ -32,5 +43,8 @@
             dsn=sentry_dsn,
             integrations=integrations,
             debug=debug,
+            before_send=functools.partial(
+                before_send, ignored_exceptions=ignored_exceptions
+            ),
             **extra_kwargs,
         )