diff --git a/swh/deposit/tests/api/test_deposit_binary.py b/swh/deposit/tests/api/test_deposit_binary.py
--- a/swh/deposit/tests/api/test_deposit_binary.py
+++ b/swh/deposit/tests/api/test_deposit_binary.py
@@ -155,6 +155,11 @@
 
     # then
     assert response.status_code == status.HTTP_400_BAD_REQUEST
+    assert (
+        b"The packaging provided something-unsupported is not supported"
+        in response.content
+    )
+
     with pytest.raises(Deposit.DoesNotExist):
         Deposit.objects.get(external_id=external_id)
 
@@ -185,6 +190,8 @@
 
     # then
     assert response.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"CONTENT_DISPOSITION header is mandatory" in response.content
+
     with pytest.raises(Deposit.DoesNotExist):
         Deposit.objects.get(external_id=external_id)
 
@@ -481,6 +488,7 @@
     )
 
     assert r.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"You can only act on deposit with status 'partial'" in r.content
 
     # adding file is no longer possible since the deposit's status
     # is ready
@@ -497,6 +505,7 @@
     )
 
     assert r.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"You can only act on deposit with status 'partial'" in r.content
 
     # replacing metadata is no longer possible since the deposit's
     # status is ready
@@ -509,6 +518,7 @@
     )
 
     assert r.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"You can only act on deposit with status 'partial'" in r.content
 
     # adding new metadata is no longer possible since the
     # deposit's status is ready
@@ -521,6 +531,7 @@
     )
 
     assert r.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"You can only act on deposit with status 'partial'" in r.content
 
     archive_content = b"some content representing archive"
     archive = InMemoryUploadedFile(
@@ -550,6 +561,7 @@
     )
 
     assert r.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"You can only act on deposit with status 'partial'" in r.content
 
     # adding new metadata is no longer possible since the
     # deposit's status is ready
@@ -560,3 +572,4 @@
     )
 
     assert r.status_code == status.HTTP_400_BAD_REQUEST
+    assert b"You can only act on deposit with status 'partial'" in r.content
diff --git a/swh/deposit/tests/api/test_deposit_delete.py b/swh/deposit/tests/api/test_deposit_delete.py
--- a/swh/deposit/tests/api/test_deposit_delete.py
+++ b/swh/deposit/tests/api/test_deposit_delete.py
@@ -81,6 +81,10 @@
     response = authenticated_client.delete(update_uri)
     # then
     assert response.status_code == status.HTTP_400_BAD_REQUEST
+    assert (
+        b"You can only act on deposit with status 'partial'" in response.content
+    )
+
     deposit = Deposit.objects.get(pk=deposit.id)
     assert deposit is not None
 
@@ -119,5 +123,9 @@
     response = authenticated_client.delete(url)
     # then
     assert response.status_code == status.HTTP_400_BAD_REQUEST
+    assert (
+        b"You can only act on deposit with status 'partial'" in response.content
+    )
+
     deposit = Deposit.objects.get(pk=deposit.id)
     assert deposit is not None
diff --git a/swh/deposit/tests/api/test_deposit_private_update_status.py b/swh/deposit/tests/api/test_deposit_private_update_status.py
--- a/swh/deposit/tests/api/test_deposit_private_update_status.py
+++ b/swh/deposit/tests/api/test_deposit_private_update_status.py
@@ -155,6 +155,7 @@
         )
 
         assert response.status_code == status.HTTP_400_BAD_REQUEST
+        assert b"Possible status in " in response.content
 
 
 def test_update_deposit_status_will_fail_with_no_status_key(
@@ -172,6 +173,7 @@
         )
 
         assert response.status_code == status.HTTP_400_BAD_REQUEST
+        assert b"The status key is mandatory with possible values" in response.content
 
 
 def test_update_deposit_status_success_without_swh_id_fail(
@@ -189,3 +191,6 @@
         )
 
         assert response.status_code == status.HTTP_400_BAD_REQUEST
+        assert (
+            b"Updating deposit status to done requires information" in response.content
+        )
diff --git a/swh/deposit/tests/api/test_deposit_update.py b/swh/deposit/tests/api/test_deposit_update.py
--- a/swh/deposit/tests/api/test_deposit_update.py
+++ b/swh/deposit/tests/api/test_deposit_update.py
@@ -10,6 +10,7 @@
 from django.urls import reverse
 from rest_framework import status
 
+from swh.deposit.api.common import ACCEPT_ARCHIVE_CONTENT_TYPES
 from swh.deposit.config import (
     DEPOSIT_STATUS_DEPOSITED,
     DEPOSIT_STATUS_PARTIAL,
@@ -474,12 +475,9 @@
         data=atom_dataset["entry-data1"],
     )
     assert response.status_code == status.HTTP_400_BAD_REQUEST
-    response_content = parse_xml(response.content)
-    msg = (
-        "Packaging format supported is restricted to "
-        + "application/zip, application/x-tar"
-    )
-    assert msg == response_content["sword:error"]["summary"]
+    assert b"Packaging format supported is restricted" in response.content
+    for supported_format in ACCEPT_ARCHIVE_CONTENT_TYPES:
+        assert supported_format.encode() in response.content
 
 
 def test_put_metadata_to_em_iri_failure(
@@ -499,12 +497,9 @@
     )
     # then
     assert response.status_code == status.HTTP_400_BAD_REQUEST
-    response_content = parse_xml(response.content)
-    msg = (
-        "Packaging format supported is restricted to "
-        + "application/zip, application/x-tar"
-    )
-    assert msg == response_content["sword:error"]["summary"]
+    assert b"Packaging format supported is restricted" in response.content
+    for supported_format in ACCEPT_ARCHIVE_CONTENT_TYPES:
+        assert supported_format.encode() in response.content
 
 
 def test_put_update_metadata_and_archive_deposit_partial_nominal(