diff --git a/jobs/templates/swh-pipeline-diff.yaml b/jobs/templates/swh-pipeline-diff.yaml
index 34cefa9..99fa975 100644
--- a/jobs/templates/swh-pipeline-diff.yaml
+++ b/jobs/templates/swh-pipeline-diff.yaml
@@ -1,44 +1,43 @@
 - job-template:
     name: "{name}/tests-on-diff"
     display-name: Phab. Diff
     project-type: pipeline
     docker_image: tox
     cypress_docker_image: cypress
     sphinx_docker_image: sphinx
     default-tox-environment: py3
     concurrent: true
     sandbox: true
-    auth-token: 'ph4br1cat0r'
+    auth-token: "ph4br1cat0r"
     phabricator_diff: true
     do_cypress: false
     timeout: 10
+    max_concurrent: 0
     properties:
       - build-discarder:
           days-to-keep: 90
           artifact-num-to-keep: 20
     parameters:
       - git-parameter:
           name: REVISION
           type: PT_REVISION
           defaultValue: master
           description: Git revision to build.
       - string:
           name: PHID
           description: PHID of the Phabricator target object on which results will be reported.
       - string:
           name: DIFF_ID
           description: ID of the Diff patch to apply, if any
       - string:
           name: REV_ID
           description: ID of the Phabricator revision, if any
       - string:
           name: STAGING_URI
           description: URI of the staging repository
       - string:
           name: TOX_ENVIRONMENT
           description: tox environment to use for the main tox run
           default: "{default-tox-environment}"
 
-    dsl:
-      !include-jinja2: swh-pipeline.groovy.j2
-
+    dsl: !include-jinja2: swh-pipeline.groovy.j2
diff --git a/jobs/templates/swh-pipeline.groovy.j2 b/jobs/templates/swh-pipeline.groovy.j2
index 8cac417..ff20db4 100644
--- a/jobs/templates/swh-pipeline.groovy.j2
+++ b/jobs/templates/swh-pipeline.groovy.j2
@@ -1,138 +1,151 @@
 pipeline {
   {% filter indent(width=2) %}
     {%- include 'includes/agent-docker.groovy.j2' -%}
   {% endfilter %}
 
+  options {
+    // require "Throttle Concurrent Builds" Jenkins plugin
+    throttleJobProperty(
+      categories: [],
+      limitOneJobWithMatchingParams: false,
+      maxConcurrentPerNode: {{ max_concurrent }},
+      maxConcurrentTotal: {{ max_concurrent }},
+      paramsToUseForLimit: '',
+      throttleEnabled: true,
+      throttleOption: 'project',
+    )
+  }
+
   environment {
     PHAB_CONDUIT_URL = 'https://forge.softwareheritage.org/api/'
   }
 
   stages {
     stage('Checkout') {
       steps {
         {% filter indent(width=8) %}
           {%- include 'includes/create-phabricator-artifacts.groovy.j2' -%}
         {% endfilter %}
         checkout([
           $class: 'GitSCM',
           branches: [[name: "${params.REVISION}"]],
           doGenerateSubmoduleConfigurations: false,
           extensions: [],
           gitTool: 'Default',
           submoduleCfg: [],
           userRemoteConfigs: [
             [url: 'https://forge.softwareheritage.org/source/{{repo_name}}.git'],
           ],
           browser: [$class: 'Phabricator', repoUrl: 'https://forge.softwareheritage.org', repo: '{{name}}']
         ])
       }
     }
 
     {%- if phabricator_diff %}
     stage('Apply phabricator diff') {
       steps {
         {% filter indent(width=8) %}
           {%- include 'includes/script-apply-phabricator-diff.groovy.j2' -%}
         {% endfilter %}
       }
     }
     {%- endif %}
 
     stage ('flake8') {
       steps {
         sh '''python3 -m tox -e flake8'''
       }
     }
 
     stage ('mypy') {
       steps {
         sh '''python3 -m tox -e mypy'''
       }
     }
 
     stage ('radon') {
       steps {
         sh  '''
           mkdir -p reports
           python3 -m radon raw --json swh/ > reports/raw_report.json
           python3 -m radon cc  --json swh/ > reports/cc_report.json
           python3 -m radon mi  --json swh/ > reports/mi_report.json
           python3 -m radon hal --json swh/ > reports/hal_report.json
           python3 -m radon cc  --xml  swh/ > reports/cc_report.xml
         '''
       }
       post {
         always {
           // Archive a few report files
           archiveArtifacts(
             allowEmptyArchive: true,
             artifacts: 'reports/*',
             fingerprint: true,
           )
 
           // Warnings NG
           recordIssues(
             enabledForFailure: true,
             tools: [
               ccm(pattern: '**/reports/cc_report.xml'),
             ],
           )
         }
       }
     }
 
     stage('Tests') {
       options {
         timeout(time: {{ timeout }}, unit: 'MINUTES')
       }
 
       parallel {
         {% filter indent(width=8) %}
           {%- include 'includes/stage-python-tests.groovy.j2' -%}
         {% endfilter %}
 
         {%- if do_cypress %}
         {% filter indent(width=8) %}
           {%- include 'includes/stage-cypress-tests.groovy.j2' -%}
         {% endfilter %}
         {%- endif %}
 
         stage('Sphinx documentation') {
           {% filter indent(width=10) %}
             {%- include 'includes/agent-docker-sphinx.groovy.j2' -%}
           {% endfilter %}
 
           steps {
             sh '''
             if tox -a | grep -x sphinx >/dev/null
             then
               tox -e sphinx
             else
               echo WARNING: no sphinx environment in tox.ini
             fi
             '''
           }
         } // sphinx doc
       } // parallel
     } // Tests stage
   } // stages
 
   post {
     always {
       step([$class: 'PhabricatorNotifier',
             commentOnSuccess: true,
             commentWithConsoleLinkOnFailure: true,
             commentFile: '.phabricator-comment',
             commentSize: '1000000',
             preserveFormatting: true,
             processLint: true,
             lintFile: '.phabricator-lint',
             lintFileSize: '1000000',
       ])
     } // always
 
     cleanup {
       cleanWs()
     }
   } // post
 } // pipeline
diff --git a/jobs/templates/swh-pipeline.yaml b/jobs/templates/swh-pipeline.yaml
index 1b49d99..053dd9b 100644
--- a/jobs/templates/swh-pipeline.yaml
+++ b/jobs/templates/swh-pipeline.yaml
@@ -1,37 +1,36 @@
 - job-template:
     name: "{name}/tests"
     display-name: "master branch"
     project-type: pipeline
     docker_image: tox
     cypress_docker_image: cypress
     sphinx_docker_image: sphinx
     default-tox-environment: py3
     concurrent: true
     triggers:
-      - timed: '@daily'
+      - timed: "@daily"
     sandbox: true
-    auth-token: 'ph4br1cat0r'
+    auth-token: "ph4br1cat0r"
     properties:
       - build-discarder:
           days-to-keep: 90
           artifact-num-to-keep: 20
     phabricator_diff: false
     do_cypress: false
     timeout: 10
+    max_concurrent: 0
     parameters:
       - git-parameter:
           name: REVISION
           type: PT_REVISION
           defaultValue: master
           description: Git revision to build.
       - string:
           name: PHID
           description: PHID of the Phabricator target object on which results will be reported.
       - string:
           name: TOX_ENVIRONMENT
           description: tox environment to use for the main tox run
           default: "{default-tox-environment}"
 
-    dsl:
-      !include-jinja2: swh-pipeline.groovy.j2
-
+    dsl: !include-jinja2: swh-pipeline.groovy.j2