diff --git a/docker/Dockerfile b/docker/Dockerfile
--- a/docker/Dockerfile
+++ b/docker/Dockerfile
@@ -21,6 +21,7 @@
     ngrep \
     rsync \
     nodejs \
+    cron \
     yarn && \
   apt-get install -y --no-install-recommends \
     r-base-core \
@@ -29,6 +30,8 @@
   rm -rf /var/lib/apt/lists/*
 
 RUN useradd -md /srv/softwareheritage -s /bin/bash swh
+RUN echo swh >> /etc/cron.allow
+RUN cron -f &
 USER swh
 
 RUN python3 -m venv /srv/softwareheritage/venv
diff --git a/docker/Dockerfile.cron b/docker/Dockerfile.cron
deleted file mode 100644
--- a/docker/Dockerfile.cron
+++ /dev/null
@@ -1,13 +0,0 @@
-FROM swh/stack
-
-USER root
-
-RUN apt-get update && apt-get install -y cron
-
-COPY ./services/swh-web/refresh-savecodenow-statuses /usr/local/bin/
-COPY ./services/swh-web/refresh-savecodenow-statuses.cron /etc/cron.d/
-
-RUN touch /var/log/refresh-statuses.log && \
-    chmod 0755 /usr/local/bin/refresh-savecodenow-statuses && \
-    chmod 0644 /etc/cron.d/refresh-savecodenow-statuses.cron && \
-    crontab /etc/cron.d/refresh-savecodenow-statuses.cron
diff --git a/docker/docker-compose.yml b/docker/docker-compose.yml
--- a/docker/docker-compose.yml
+++ b/docker/docker-compose.yml
@@ -240,15 +240,7 @@
     volumes:
       - "./conf/web.yml:/web.yml:ro"
       - "./services/swh-web/entrypoint.sh:/entrypoint.sh:ro"
-
-  swh-web-cron:
-    build: ./
-    image: swh/cron
-    depends_on:
-      - swh-web
-    entrypoint: ["cron", "-f"]
-    volumes:
-      - "./conf/web.yml:/web.yml:ro"
+      - "./services/swh-web/refresh-savecodenow-statuses.cron:/etc/cron.d/refresh-savecodenow-statuses.cron"
 
   swh-deposit-db:
     image: postgres:12
diff --git a/docker/services/swh-web/entrypoint.sh b/docker/services/swh-web/entrypoint.sh
--- a/docker/services/swh-web/entrypoint.sh
+++ b/docker/services/swh-web/entrypoint.sh
@@ -40,6 +40,10 @@
             popd
         fi
 
+        # Trigger periodic update of save code now status
+        crontab -u swh /etc/cron.d/refresh-savecodenow-statuses.cron
+        crontab -u swh -l
+
         echo "Migrating db using ${DJANGO_SETTINGS_MODULE}"
         django-admin migrate --settings=${DJANGO_SETTINGS_MODULE}
 
diff --git a/docker/services/swh-web/refresh-savecodenow-statuses b/docker/services/swh-web/refresh-savecodenow-statuses
deleted file mode 100644
--- a/docker/services/swh-web/refresh-savecodenow-statuses
+++ /dev/null
@@ -1,8 +0,0 @@
-#!/usr/bin/env bash
-
-set -x
-
-export DJANGO_SETTINGS_MODULE=swh.web.settings.production
-export SWH_CONFIG_FILENAME=/web.yml
-
-/srv/softwareheritage/venv/bin/django-admin refresh_savecodenow_statuses
diff --git a/docker/services/swh-web/refresh-savecodenow-statuses.cron b/docker/services/swh-web/refresh-savecodenow-statuses.cron
--- a/docker/services/swh-web/refresh-savecodenow-statuses.cron
+++ b/docker/services/swh-web/refresh-savecodenow-statuses.cron
@@ -1 +1 @@
-* * * * * (date && /usr/local/bin/refresh-savecodenow-statuses 2>&1) >> /var/log/refresh-statuses.log
+* * * * * (date && /srv/softwareheritage/venv/bin/django-admin refresh_savecodenow_statuses 2>&1) >> /tmp/refresh-statuses.log