diff --git a/swh/storage/cassandra/storage.py b/swh/storage/cassandra/storage.py
--- a/swh/storage/cassandra/storage.py
+++ b/swh/storage/cassandra/storage.py
@@ -139,7 +139,7 @@
         self._consistency_level = consistency_level
         self._set_cql_runner()
         self.journal_writer: JournalWriter = JournalWriter(journal_writer)
-        self.objstorage: ObjStorage = ObjStorage(objstorage)
+        self.objstorage: ObjStorage = ObjStorage(self, objstorage)
         self._allow_overwrite = allow_overwrite
 
         if directory_entries_insert_algo not in DIRECTORY_ENTRIES_INSERT_ALGOS:
@@ -275,7 +275,7 @@
     def content_add_metadata(self, content: List[Content]) -> Dict[str, int]:
         return self._content_add(content, with_data=False)
 
-    def content_get_data(self, content: Sha1) -> Optional[bytes]:
+    def content_get_data(self, content: Union[Sha1, HashDict]) -> Optional[bytes]:
         # FIXME: Make this method support slicing the `data`
         return self.objstorage.content_get(content)
 
diff --git a/swh/storage/in_memory.py b/swh/storage/in_memory.py
--- a/swh/storage/in_memory.py
+++ b/swh/storage/in_memory.py
@@ -836,7 +836,7 @@
 
     def reset(self):
         self._cql_runner = InMemoryCqlRunner()
-        self.objstorage = ObjStorage({"cls": "memory"})
+        self.objstorage = ObjStorage(self, {"cls": "memory"})
 
     def check_config(self, *, check_write: bool) -> bool:
         return True
diff --git a/swh/storage/interface.py b/swh/storage/interface.py
--- a/swh/storage/interface.py
+++ b/swh/storage/interface.py
@@ -5,7 +5,7 @@
 
 import datetime
 from enum import Enum
-from typing import Any, Dict, Iterable, List, Optional, Sequence, Tuple, TypeVar
+from typing import Any, Dict, Iterable, List, Optional, Sequence, Tuple, TypeVar, Union
 
 import attr
 from typing_extensions import Protocol, TypedDict, runtime_checkable
@@ -181,11 +181,11 @@
         ...
 
     @remote_api_endpoint("content/data")
-    def content_get_data(self, content: Sha1) -> Optional[bytes]:
+    def content_get_data(self, content: Union[HashDict, Sha1]) -> Optional[bytes]:
         """Given a content identifier, returns its associated data if any.
 
         Args:
-            content: sha1 identifier
+            content: dict of hashes (or just sha1 identifier)
 
         Returns:
              raw content data (bytes)
diff --git a/swh/storage/objstorage.py b/swh/storage/objstorage.py
--- a/swh/storage/objstorage.py
+++ b/swh/storage/objstorage.py
@@ -1,14 +1,15 @@
-# Copyright (C) 2020 The Software Heritage developers
+# Copyright (C) 2020-2022 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
 
-from typing import Dict, Iterable, Optional
+from typing import Dict, Iterable, Optional, Union, cast
 
+from swh.model.hashutil import DEFAULT_ALGORITHMS
 from swh.model.model import Content, MissingData
 from swh.objstorage.exc import ObjNotFoundError
 from swh.objstorage.factory import get_objstorage
-from swh.storage.interface import Sha1
+from swh.storage.interface import HashDict, Sha1
 
 from .exc import StorageArgumentException
 
@@ -19,7 +20,8 @@
 
     """
 
-    def __init__(self, objstorage_config: Dict):
+    def __init__(self, storage, objstorage_config: Dict):
+        self.storage = storage
         self.objstorage = get_objstorage(**objstorage_config)
 
     def __getattr__(self, key):
@@ -27,7 +29,7 @@
             raise AttributeError(key)
         return getattr(self.objstorage, key)
 
-    def content_get(self, obj_id: Sha1) -> Optional[bytes]:
+    def content_get(self, obj_id: Union[Sha1, HashDict]) -> Optional[bytes]:
         """Retrieve data associated to the content from the objstorage
 
         Args:
@@ -37,8 +39,26 @@
             associated content's data if any, None otherwise.
 
         """
+        hashes: HashDict
+        if isinstance(obj_id, bytes):
+            hashes = {"sha1": obj_id}
+        else:
+            hashes = obj_id
+        if set(hashes) < DEFAULT_ALGORITHMS:
+            # If some hashes are missing, query the database to fill blanks
+            candidates = self.storage.content_find(hashes)
+            if candidates:
+                # There may be more than one in case of collision; but we cannot
+                # do anything about it here
+                hashes = cast(HashDict, candidates[0].hashes())
+            else:
+                # we will pass the partial hash dict to the objstorage, which
+                # will do the best it can with it. Usually, this will return None,
+                # as objects missing from the storage DB are unlikely to be present in the
+                # objstorage
+                pass
         try:
-            data = self.objstorage.get(obj_id)
+            data = self.objstorage.get(hashes)
         except ObjNotFoundError:
             data = None
 
diff --git a/swh/storage/postgresql/storage.py b/swh/storage/postgresql/storage.py
--- a/swh/storage/postgresql/storage.py
+++ b/swh/storage/postgresql/storage.py
@@ -11,7 +11,7 @@
 import itertools
 import logging
 import operator
-from typing import Any, Counter, Dict, Iterable, List, Optional, Sequence, Tuple
+from typing import Any, Counter, Dict, Iterable, List, Optional, Sequence, Tuple, Union
 
 import attr
 import psycopg2
@@ -163,7 +163,7 @@
         except psycopg2.OperationalError as e:
             raise StorageDBError(e)
         self.journal_writer = JournalWriter(journal_writer)
-        self.objstorage = ObjStorage(objstorage)
+        self.objstorage = ObjStorage(self, objstorage)
         self.query_options = query_options
         self._flavor: Optional[str] = None
 
@@ -341,7 +341,7 @@
             "content:add": len(contents),
         }
 
-    def content_get_data(self, content: Sha1) -> Optional[bytes]:
+    def content_get_data(self, content: Union[HashDict, Sha1]) -> Optional[bytes]:
         # FIXME: Make this method support slicing the `data`
         return self.objstorage.content_get(content)
 
diff --git a/swh/storage/pytest_plugin.py b/swh/storage/pytest_plugin.py
--- a/swh/storage/pytest_plugin.py
+++ b/swh/storage/pytest_plugin.py
@@ -48,10 +48,21 @@
 
 
 @pytest.fixture
-def swh_storage(swh_storage_backend_config):
+def swh_storage_backend(swh_storage_backend_config):
+    """
+    By default, this fixture aliases ``swh_storage``. However, when ``swh_storage``
+    is overridden to be a proxy storage, this fixture returns the storage instance
+    behind all proxies.
+
+    This is useful to introspect the state of backends from proxy tests"""
     return get_storage(**swh_storage_backend_config)
 
 
+@pytest.fixture
+def swh_storage(swh_storage_backend):
+    return swh_storage_backend
+
+
 @pytest.fixture
 def sample_data() -> StorageData:
     """Pre-defined sample storage object data to manipulate
diff --git a/swh/storage/tests/storage_tests.py b/swh/storage/tests/storage_tests.py
--- a/swh/storage/tests/storage_tests.py
+++ b/swh/storage/tests/storage_tests.py
@@ -238,6 +238,58 @@
             swh_storage.refresh_stat_counters()
             assert swh_storage.stat_counters()["content"] == 1
 
+    @pytest.mark.parametrize("algo", sorted(DEFAULT_ALGORITHMS))
+    def test_content_get_data_single_hash_dict(
+        self, swh_storage, swh_storage_backend, sample_data, mocker, algo
+    ):
+        cont = sample_data.content
+
+        swh_storage.content_add([cont])
+
+        content_find = mocker.patch.object(
+            swh_storage_backend, "content_find", wraps=swh_storage_backend.content_find
+        )
+        assert swh_storage.content_get_data({algo: cont.get_hash(algo)}) == cont.data
+
+        assert len(content_find.mock_calls) == 1
+
+    def test_content_get_data_two_hash_dict(
+        self, swh_storage, swh_storage_backend, sample_data, mocker
+    ):
+        cont = sample_data.content
+
+        swh_storage.content_add([cont])
+
+        content_find = mocker.patch.object(
+            swh_storage_backend, "content_find", wraps=swh_storage_backend.content_find
+        )
+
+        combinations = list(itertools.combinations(sorted(DEFAULT_ALGORITHMS), 2))
+        for (algo1, algo2) in combinations:
+            assert (
+                swh_storage.content_get_data(
+                    {algo1: cont.get_hash(algo1), algo2: cont.get_hash(algo2)}
+                )
+                == cont.data
+            )
+        assert len(content_find.mock_calls) == len(combinations)
+
+    def test_content_get_data_full_dict(
+        self, swh_storage, swh_storage_backend, sample_data, mocker
+    ):
+        cont = sample_data.content
+
+        swh_storage.content_add([cont])
+
+        content_find = mocker.patch.object(
+            swh_storage_backend, "content_find", wraps=swh_storage_backend.content_find
+        )
+        assert swh_storage.content_get_data(cont.hashes()) == cont.data
+        assert len(content_find.mock_calls) == 0, (
+            "content_get_data() needlessly called content_find(), "
+            "as all hashes were provided as argument"
+        )
+
     def test_content_get_data_missing(self, swh_storage, sample_data):
         cont, cont2 = sample_data.contents[:2]
 
diff --git a/swh/storage/tests/test_api_client.py b/swh/storage/tests/test_api_client.py
--- a/swh/storage/tests/test_api_client.py
+++ b/swh/storage/tests/test_api_client.py
@@ -63,6 +63,11 @@
     storage.journal_writer = journal_writer
 
 
+@pytest.fixture
+def swh_storage_backend(app_server, swh_storage):
+    return app_server.storage
+
+
 class TestStorageApi(_TestStorage):
     @pytest.mark.skip(
         'The "person" table of the pgsql is a legacy thing, and not '
diff --git a/swh/storage/tests/test_tenacious.py b/swh/storage/tests/test_tenacious.py
--- a/swh/storage/tests/test_tenacious.py
+++ b/swh/storage/tests/test_tenacious.py
@@ -36,7 +36,7 @@
 
 
 @pytest.fixture
-def swh_storage_backend_config2():
+def swh_storage_backend_config():
     yield {
         "cls": "memory",
         "journal_writer": {
@@ -46,21 +46,17 @@
 
 
 @pytest.fixture
-def swh_storage():
+def swh_storage(swh_storage_backend, swh_storage_backend_config):
     storage_config = {
         "cls": "pipeline",
         "steps": [
             {"cls": "tenacious"},
-            {
-                "cls": "memory",
-                "journal_writer": {
-                    "cls": "memory",
-                },
-            },
+            swh_storage_backend_config,
         ],
     }
 
     storage = get_storage(**storage_config)
+    storage.storage = swh_storage_backend  # use the same instance of the in-mem backend
     storage.journal_writer = storage.storage.journal_writer
     return storage