diff --git a/swh/objstorage/replayer/replay.py b/swh/objstorage/replayer/replay.py
--- a/swh/objstorage/replayer/replay.py
+++ b/swh/objstorage/replayer/replay.py
@@ -3,6 +3,8 @@
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
 
+from concurrent.futures import FIRST_EXCEPTION, ThreadPoolExecutor
+from concurrent.futures import wait as futures_wait
 import logging
 from time import time
 from typing import Callable, Dict, List, Optional
@@ -216,6 +218,7 @@
     dst: ObjStorage,
     exclude_fn: Optional[Callable[[dict], bool]] = None,
     check_dst: bool = True,
+    concurrency: int = 16,
 ):
     """
     Takes a list of records from Kafka (see
@@ -268,52 +271,66 @@
     nb_failures = 0
     t0 = time()
 
-    for (object_type, objects) in all_objects.items():
-        if object_type != "content":
-            logger.warning(
-                "Received a series of %s, this should not happen", object_type
+    def _copy_object(obj):
+        nonlocal nb_skipped
+        nonlocal nb_failures
+
+        obj_id = obj[ID_HASH_ALGO]
+        if obj["status"] != "visible":
+            nb_skipped += 1
+            logger.debug("skipped %s (status=%s)", hash_to_hex(obj_id), obj["status"])
+            statsd.increment(
+                CONTENT_OPERATIONS_METRIC,
+                tags={"decision": "skipped", "status": obj["status"]},
             )
-            continue
-        for obj in objects:
-            obj_id = obj[ID_HASH_ALGO]
-            if obj["status"] != "visible":
-                nb_skipped += 1
-                logger.debug(
-                    "skipped %s (status=%s)", hash_to_hex(obj_id), obj["status"]
-                )
-                statsd.increment(
-                    CONTENT_OPERATIONS_METRIC,
-                    tags={"decision": "skipped", "status": obj["status"]},
-                )
-            elif exclude_fn and exclude_fn(obj):
+        elif exclude_fn and exclude_fn(obj):
+            nb_skipped += 1
+            logger.debug("skipped %s (manually excluded)", hash_to_hex(obj_id))
+            statsd.increment(CONTENT_OPERATIONS_METRIC, tags={"decision": "excluded"})
+        elif check_dst and obj_in_objstorage(obj_id, dst):
+            nb_skipped += 1
+            logger.debug("skipped %s (in dst)", hash_to_hex(obj_id))
+            statsd.increment(CONTENT_OPERATIONS_METRIC, tags={"decision": "in_dst"})
+        else:
+            try:
+                copied = copy_object(obj_id, src, dst)
+            except ObjNotFoundError:
                 nb_skipped += 1
-                logger.debug("skipped %s (manually excluded)", hash_to_hex(obj_id))
                 statsd.increment(
-                    CONTENT_OPERATIONS_METRIC, tags={"decision": "excluded"}
+                    CONTENT_OPERATIONS_METRIC, tags={"decision": "not_in_src"}
                 )
-            elif check_dst and obj_in_objstorage(obj_id, dst):
-                nb_skipped += 1
-                logger.debug("skipped %s (in dst)", hash_to_hex(obj_id))
-                statsd.increment(CONTENT_OPERATIONS_METRIC, tags={"decision": "in_dst"})
             else:
-                try:
-                    copied = copy_object(obj_id, src, dst)
-                except ObjNotFoundError:
-                    nb_skipped += 1
+                if copied is None:
+                    nb_failures += 1
                     statsd.increment(
-                        CONTENT_OPERATIONS_METRIC, tags={"decision": "not_in_src"}
+                        CONTENT_OPERATIONS_METRIC, tags={"decision": "failed"}
                     )
                 else:
-                    if copied is None:
-                        nb_failures += 1
-                        statsd.increment(
-                            CONTENT_OPERATIONS_METRIC, tags={"decision": "failed"}
-                        )
-                    else:
-                        vol.append(copied)
-                        statsd.increment(
-                            CONTENT_OPERATIONS_METRIC, tags={"decision": "copied"}
-                        )
+                    vol.append(copied)
+                    statsd.increment(
+                        CONTENT_OPERATIONS_METRIC, tags={"decision": "copied"}
+                    )
+
+    with ThreadPoolExecutor(max_workers=concurrency) as pool:
+        futures = []
+        for (object_type, objects) in all_objects.items():
+            if object_type != "content":
+                logger.warning(
+                    "Received a series of %s, this should not happen", object_type
+                )
+                continue
+            for obj in objects:
+                futures.append(pool.submit(_copy_object, obj=obj))
+
+    futures_wait(futures, return_when=FIRST_EXCEPTION)
+    for f in futures:
+        if f.running():
+            continue
+        exc = f.exception()
+        if exc:
+            pool.shutdown(wait=False)
+            f.result()
+            raise exc
 
     dt = time() - t0
     logger.info(