diff --git a/CHANGELOG.md b/CHANGELOG.md
index d855dab..88a968c 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,3 +1,11 @@
+## Unreleased
+
+* [fix] Avoid running Kubernetes CronJob instances concurrently by
+  default: add the `BACKUP_K8S_CRONJOB_CONCURRENCYPOLICY` setting
+  and default it to `Forbid` (rather than
+  [the Kubernetes default](https://kubernetes.io/docs/concepts/workloads/controllers/cron-jobs/#concurrency-policy),
+  `Allow`).
+
 ## Version 2.1.0 (2023-08-22)
 
 * [Enhancement] Support Tutor 16, Open edX Palm and Python 3.11.
diff --git a/README.md b/README.md
index 5630d2e..a3d1bbb 100644
--- a/README.md
+++ b/README.md
@@ -188,6 +188,7 @@ Configuration
 * `BACKUP_K8S_CRONJOB_RESTORE_ENABLE` (default: `false`, periodic restore is disabled.)
 * `BACKUP_K8S_CRONJOB_RESTORE_SCHEDULE` (default: `"30 0 * * *"`, once a day at 30 mins past
    midnight)
+* `BACKUP_K8S_CRONJOB_CONCURRENCYPOLICY` (default: `"Forbid"`, see [the Kubernetes documentation](https://kubernetes.io/docs/concepts/workloads/controllers/cron-jobs/#concurrency-policy) for other available options)
 * `BACKUP_K8S_USE_EPHEMERAL_VOLUMES` (default: `false`)
 * `BACKUP_K8S_EPHEMERAL_VOLUME_SIZE` (default: `10Gi`)
 
diff --git a/tutorbackup/patches/k8s-jobs b/tutorbackup/patches/k8s-jobs
index 502b157..e0d4438 100644
--- a/tutorbackup/patches/k8s-jobs
+++ b/tutorbackup/patches/k8s-jobs
@@ -111,6 +111,7 @@ spec:
   schedule: '{{ BACKUP_K8S_CRONJOB_BACKUP_SCHEDULE }}'
   startingDeadlineSeconds: {{ BACKUP_K8S_CRONJOB_STARTING_DEADLINE_SECONDS }}
   successfulJobsHistoryLimit: {{ BACKUP_K8S_CRONJOB_HISTORYLIMIT_SUCCESS }}
+  concurrencyPolicy: '{{ BACKUP_K8S_CRONJOB_CONCURRENCYPOLICY }}'
   jobTemplate:
     spec:
       template:
@@ -217,6 +218,7 @@ spec:
   schedule: '{{ BACKUP_K8S_CRONJOB_RESTORE_SCHEDULE }}'
   startingDeadlineSeconds: {{ BACKUP_K8S_CRONJOB_STARTING_DEADLINE_SECONDS }}
   successfulJobsHistoryLimit: {{ BACKUP_K8S_CRONJOB_HISTORYLIMIT_SUCCESS }}
+  concurrencyPolicy: '{{ BACKUP_K8S_CRONJOB_CONCURRENCYPOLICY }}'
   jobTemplate:
     spec:
       template:
diff --git a/tutorbackup/plugin.py b/tutorbackup/plugin.py
index caa16e1..e9092e9 100644
--- a/tutorbackup/plugin.py
+++ b/tutorbackup/plugin.py
@@ -21,6 +21,7 @@
         "K8S_CRONJOB_BACKUP_SCHEDULE": "0 0 * * *",
         "K8S_CRONJOB_RESTORE_ENABLE": False,
         "K8S_CRONJOB_RESTORE_SCHEDULE": "30 0 * * *",
+        "K8S_CRONJOB_CONCURRENCYPOLICY": "Forbid",
         "K8S_USE_EPHEMERAL_VOLUMES": False,
         "K8S_EPHEMERAL_VOLUME_SIZE": "10Gi",
         "S3_HOST": "{{ S3_HOST | default('') }}",