diff --git a/jobs/templates/swh-pipeline.groovy.j2 b/jobs/templates/swh-pipeline.groovy.j2
--- a/jobs/templates/swh-pipeline.groovy.j2
+++ b/jobs/templates/swh-pipeline.groovy.j2
@@ -81,40 +81,42 @@
       }
     } // static analysis
 
-    stage('Tests') {
-      options {
-        timeout(time: 20, unit: 'MINUTES')
-      }
+    parallel {
+      stage('Tests') {
+        options {
+          timeout(time: 20, unit: 'MINUTES')
+        }
 
-      parallel {
-        {% filter indent(width=8) %}
-          {%- include 'includes/stage-python-tests.groovy.j2' -%}
-        {% endfilter %}
+        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 %}
+          {%- if do_cypress %}
+          {% filter indent(width=8) %}
+            {%- include 'includes/stage-cypress-tests.groovy.j2' -%}
+          {% endfilter %}
+          {%- endif %}
+        }
       }
-    }
 
-    stage('Sphinx documentation') {
-      {% filter indent(width=6) %}
-        {%- include 'includes/agent-docker-sphinx.groovy.j2' -%}
-      {% endfilter %}
+      stage('Sphinx documentation') {
+        {% filter indent(width=6) %}
+          {%- 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
+        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
   } // stages
 
   post {