diff --git a/jobs/templates/swh-pypi.groovy.j2 b/jobs/templates/swh-pypi.groovy.j2
index 282f910..0b35403 100644
--- a/jobs/templates/swh-pypi.groovy.j2
+++ b/jobs/templates/swh-pypi.groovy.j2
@@ -1,112 +1,95 @@
 def module_name = '{{repo_name}}'.replace('-', '.')
 
 def PYPI_UPLOAD_HOST
 
 switch (params.PYPI_HOST) {
   case 'pypi.org':
     PYPI_UPLOAD_HOST = 'upload.pypi.org'
     break
   default:
     PYPI_UPLOAD_HOST = params.PYPI_HOST
     break
 }
 
 pipeline {
   {% filter indent(width=2) %}
     {%- include 'includes/agent-docker.groovy.j2' -%}
   {% endfilter %}
 
   stages {
     stage('Run tests') {
       when {
         expression { return !params.SKIP_TESTS }
         beforeAgent true
       }
       agent none
       steps {
         build(
           job: '/{{name}}/tests',
           parameters: [
             string(name: 'REVISION', value: params.GIT_TAG),
           ],
           propagate: !params.IGNORE_TESTS,
         )
       }
     }
 
-    stage('Run cypress tests') {
-      when {
-        expression { '{{repo_name}}' == 'swh-web' && !params.SKIP_TESTS }
-        beforeAgent true
-      }
-      agent none
-      steps {
-        build(
-          job: '/{{name}}/cypress',
-          parameters: [
-            string(name: 'REVISION', value: params.GIT_TAG),
-          ],
-          propagate: !params.IGNORE_TESTS,
-        )
-      }
-    }
-
     stage('Checkout') {
       steps {
         checkout([$class: 'GitSCM',
                   branches: [[name: params.GIT_TAG]],
                   doGenerateSubmoduleConfigurations: false,
                   extensions: [],
                   gitTool: 'Default',
                   submoduleCfg: [],
                   userRemoteConfigs: [[url: 'https://forge.softwareheritage.org/source/{{repo_name}}.git']]
         ])
       }
     }
 
     stage('Build') {
       steps {
         sh '''
           # Build javascript assets
           if [ -f yarn.lock ]; then
             yarn install --frozen-lockfile
             yarn build
           fi
 
           # Build java assets
           if [ -d java ]; then
             for pom in $( find java/ -name pom.xml ) ; do
               mvn -f $pom compile assembly:single
             done
           fi
 
           python3 setup.py sdist bdist_wheel
         '''
         archiveArtifacts allowEmptyArchive: true,
           artifacts: 'dist/*',
           fingerprint: true
       }
     }
 
     stage('Publish') {
       when {
         anyOf {
           expression { return params.FORCE_UPLOAD }
           expression {
             LASTV=sh(returnStdout: true,
                      script:"curl -s https://${params.PYPI_HOST}/pypi/${module_name}/json | jq -r .info.version || true").trim()
             return 'v'+LASTV != params.GIT_TAG
             }
         }
       }
       steps {
         withCredentials([
           usernamePassword(credentialsId: PYPI_UPLOAD_HOST,
                            usernameVariable: 'TWINE_USERNAME',
                            passwordVariable: 'TWINE_PASSWORD')]) {
           sh "python3 -m twine upload --repository-url https://${PYPI_UPLOAD_HOST}/legacy/ dist/*"
         }
       }
     }
   }
 }