diff --git a/jobs/templates/includes/stage-python-tests.groovy.j2 b/jobs/templates/includes/stage-python-tests.groovy.j2
index 6a69e1d..f1f6494 100644
--- a/jobs/templates/includes/stage-python-tests.groovy.j2
+++ b/jobs/templates/includes/stage-python-tests.groovy.j2
@@ -1,35 +1,32 @@
-stage('Unit tests') {
-  options {
-    timeout(time: 20, unit: 'MINUTES')
-  }
+stage('Python tests') {
   steps {
     sh '''
     python3 -m tox -e $TOX_ENVIRONMENT -- \
       --cov-report=xml \
       --junit-xml=test-results.xml \
       -v
     '''
   }
   post {
     always {
       archiveArtifacts(
         allowEmptyArchive: true,
         artifacts: '*.xml',
         fingerprint: true,
       )
 
       publishCoverage(
         adapters: [
           coberturaAdapter(path: 'coverage.xml'),
         ],
         tag: 'pytest',
       )
 
       // JUnit report
       junit(
         allowEmptyResults: true,
         testResults: 'test-results.xml',
       )
     }
   } // post
 } // unit tests
diff --git a/jobs/templates/swh-pipeline.groovy.j2 b/jobs/templates/swh-pipeline.groovy.j2
index f9ecb95..76b2568 100644
--- a/jobs/templates/swh-pipeline.groovy.j2
+++ b/jobs/templates/swh-pipeline.groovy.j2
@@ -1,108 +1,112 @@
 pipeline {
   {% filter indent(width=2) %}
     {%- include 'includes/agent-docker.groovy.j2' -%}
   {% endfilter %}
 
   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 %}
     {% filter indent(width=4) %}
       {%- include 'includes/stage-apply-phabricator-diff.groovy.j2' -%}
     {% endfilter %}
     {%- endif %}
 
     stage('Static analysis') {
       steps {
         echo 'flake8'
         sh '''python3 -m tox -e flake8'''
 
         echo 'mypy'
         sh '''if python3 -m tox -a 2>/dev/null | grep -qx mypy ; then python3 -m tox -e mypy ; fi'''
 
         echo 'radon';
         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'),
             ],
           )
         }
       }
     } // static analysis
 
     stage('Tests') {
+      options {
+        timeout(time: 20, 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 %}
       }
     }
   } // 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