diff --git a/swh/web/api/apiresponse.py b/swh/web/api/apiresponse.py
--- a/swh/web/api/apiresponse.py
+++ b/swh/web/api/apiresponse.py
@@ -8,8 +8,6 @@
 import traceback
 from typing import Any, Dict, Optional
 
-import sentry_sdk
-
 from django.http import HttpResponse
 from django.shortcuts import render
 from django.utils.cache import add_never_cache_headers
@@ -21,7 +19,13 @@
 
 from swh.storage.exc import StorageAPIError, StorageDBError
 from swh.web.api import utils
-from swh.web.common.exc import BadInputExc, ForbiddenExc, LargePayloadExc, NotFoundExc
+from swh.web.common.exc import (
+    BadInputExc,
+    ForbiddenExc,
+    LargePayloadExc,
+    NotFoundExc,
+    sentry_capture_exception,
+)
 from swh.web.common.utils import gen_path_info, shorten_path
 from swh.web.config import get_config
 
@@ -220,6 +224,6 @@
 ) -> Optional[HttpResponse]:
     """Custom DRF exception handler used to generate API error responses.
     """
-    sentry_sdk.capture_exception(exc)
+    sentry_capture_exception(exc)
     doc_data = getattr(exc, "doc_data", None)
     return error_response(context["request"], exc, doc_data)
diff --git a/swh/web/common/exc.py b/swh/web/common/exc.py
--- a/swh/web/common/exc.py
+++ b/swh/web/common/exc.py
@@ -8,6 +8,7 @@
 
 import sentry_sdk
 
+from django.core import exceptions
 from django.shortcuts import render
 from django.utils.html import escape
 from django.utils.safestring import mark_safe
@@ -27,7 +28,7 @@
     pass
 
 
-class NotFoundExc(Exception):
+class NotFoundExc(exceptions.ObjectDoesNotExist):
     """Good request to the api but no result were found.
 
     Example: Asking a content with the right identifier format but
@@ -38,7 +39,7 @@
     pass
 
 
-class ForbiddenExc(Exception):
+class ForbiddenExc(exceptions.PermissionDenied):
     """Good request to the api, forbidden result to return due to enforce
        policy.
 
@@ -128,12 +129,24 @@
     return _generate_error_page(request, 500, error_description)
 
 
+def sentry_capture_exception(exc):
+    if not isinstance(
+        exc,
+        (
+            exceptions.ObjectDoesNotExist,
+            exceptions.DisallowedHost,
+            exceptions.PermissionDenied,
+        ),
+    ):
+        sentry_sdk.capture_exception(exc)
+
+
 def handle_view_exception(request, exc):
     """
     Function used to generate an error page when an exception
     was raised inside a swh-web browse view.
     """
-    sentry_sdk.capture_exception(exc)
+    sentry_capture_exception(exc)
     error_code = 500
     error_description = "%s: %s" % (type(exc).__name__, str(exc))
     if get_config()["debug"]:
diff --git a/swh/web/common/middlewares.py b/swh/web/common/middlewares.py
--- a/swh/web/common/middlewares.py
+++ b/swh/web/common/middlewares.py
@@ -5,9 +5,8 @@
 
 
 from htmlmin import minify
-import sentry_sdk
 
-from swh.web.common.exc import handle_view_exception
+from swh.web.common.exc import handle_view_exception, sentry_capture_exception
 from swh.web.common.utils import prettify_html
 
 
@@ -51,7 +50,7 @@
                 )
                 response.content = minified_html.encode("utf-8")
             except Exception as exc:
-                sentry_sdk.capture_exception(exc)
+                sentry_capture_exception(exc)
         return response