diff --git a/swh/journal/tests/test_inmemory.py b/swh/journal/tests/test_inmemory.py
--- a/swh/journal/tests/test_inmemory.py
+++ b/swh/journal/tests/test_inmemory.py
@@ -1,3 +1,8 @@
+# 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
+
 import pytest
 
 from swh.journal.writer import model_object_dict_sanitizer
@@ -11,34 +16,22 @@
         value_sanitizer=model_object_dict_sanitizer
     )
     expected = []
+    priv_expected = []
 
     for object_type, objects in TEST_OBJECTS.items():
         writer.write_additions(object_type, objects)
 
         for object in objects:
-            expected.append((object_type, object))
+            if object.anonymize():
+                expected.append((object_type, object.anonymize()))
+                priv_expected.append((object_type, object))
+            else:
+                expected.append((object_type, object))
 
-    assert list(writer.privileged_objects) == []
+    assert set(priv_expected) == set(writer.privileged_objects)
     assert set(expected) == set(writer.objects)
 
 
-def test_write_additions_with_privileged_test_objects():
-    writer = InMemoryJournalWriter[BaseModel](
-        value_sanitizer=model_object_dict_sanitizer
-    )
-
-    expected = []
-
-    for object_type, objects in TEST_OBJECTS.items():
-        writer.write_additions(object_type, objects, True)
-
-        for object in objects:
-            expected.append((object_type, object))
-
-    assert list(writer.objects) == []
-    assert set(expected) == set(writer.privileged_objects)
-
-
 def test_write_addition_errors_without_unique_key():
     writer = InMemoryJournalWriter[BaseModel](
         value_sanitizer=model_object_dict_sanitizer
diff --git a/swh/journal/writer/inmemory.py b/swh/journal/writer/inmemory.py
--- a/swh/journal/writer/inmemory.py
+++ b/swh/journal/writer/inmemory.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
@@ -27,19 +27,17 @@
         self.objects = self.manager.list()
         self.privileged_objects = self.manager.list()
 
-    def write_addition(
-        self, object_type: str, object_: TValue, privileged: bool = False
-    ) -> None:
+    def write_addition(self, object_type: str, object_: TValue) -> None:
         object_.unique_key()  # Check this does not error, to mimic the kafka writer
-        if privileged:
+        anon_object_ = object_.anonymize()
+        if anon_object_ is not None:
             self.privileged_objects.append((object_type, object_))
+            self.objects.append((object_type, anon_object_))
         else:
             self.objects.append((object_type, object_))
 
     write_update = write_addition
 
-    def write_additions(
-        self, object_type: str, objects: List[TValue], privileged: bool = False
-    ) -> None:
+    def write_additions(self, object_type: str, objects: List[TValue]) -> None:
         for object_ in objects:
-            self.write_addition(object_type, object_, privileged)
+            self.write_addition(object_type, object_)
diff --git a/swh/journal/writer/stream.py b/swh/journal/writer/stream.py
--- a/swh/journal/writer/stream.py
+++ b/swh/journal/writer/stream.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2021 The Software Heritage developers
+# Copyright (C) 2021-2022 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
@@ -31,17 +31,13 @@
         self.output = output_stream
         self.value_sanitizer = value_sanitizer
 
-    def write_addition(
-        self, object_type: str, object_: TValue, privileged: bool = False
-    ) -> None:
+    def write_addition(self, object_type: str, object_: TValue) -> None:
         object_.unique_key()  # Check this does not error, to mimic the kafka writer
         dict_ = self.value_sanitizer(object_type, object_.to_dict())
         self.output.write(value_to_kafka((object_type, dict_)))
 
     write_update = write_addition
 
-    def write_additions(
-        self, object_type: str, objects: List[TValue], privileged: bool = False
-    ) -> None:
+    def write_additions(self, object_type: str, objects: List[TValue]) -> None:
         for object_ in objects:
-            self.write_addition(object_type, object_, privileged)
+            self.write_addition(object_type, object_)