diff --git a/app/jobs/cron/purge_old_brouillon_dossiers_job.rb b/app/jobs/cron/hide_old_brouillon_dossiers_job.rb
similarity index 56%
rename from app/jobs/cron/purge_old_brouillon_dossiers_job.rb
rename to app/jobs/cron/hide_old_brouillon_dossiers_job.rb
index 147b16a29..9ffb87026 100644
--- a/app/jobs/cron/purge_old_brouillon_dossiers_job.rb
+++ b/app/jobs/cron/hide_old_brouillon_dossiers_job.rb
@@ -1,12 +1,13 @@
 # frozen_string_literal: true
 
-class Cron::PurgeOldBrouillonDossiersJob < Cron::CronJob
-  self.schedule_expression = "every day at 5:30"
+class Cron::HideOldBrouillonDossiersJob < Cron::CronJob
+  self.schedule_expression = "every day at 21:00"
 
   def perform
     Dossier
+      .visible_by_user
       .state_brouillon
-      .where(updated_at: ..(3.months + 2.weeks).ago)
+      .where(updated_at: ..(3.months + 2.weeks).ago, notified_soon_deleted_sent_at: ..2.weeks.ago)
       .find_each do |dossier|
         dossier.hide_and_keep_track!(:automatic, :not_modified_for_a_long_time)
         DossierMailer.notify_old_brouillon_after_deletion(dossier).deliver_later
diff --git a/app/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job.rb b/app/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job.rb
index 95e54617c..61dc27654 100644
--- a/app/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job.rb
+++ b/app/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job.rb
@@ -5,6 +5,7 @@ class Cron::NotifyOldBrouillonDossiersSoonDeletedJob < Cron::CronJob
 
   def perform
     Dossier
+      .visible_by_user
       .state_brouillon
       .where(updated_at: ..3.months.ago)
       .where("notified_soon_deleted_sent_at IS NULL OR notified_soon_deleted_sent_at < updated_at")
diff --git a/spec/jobs/cron/purge_old_brouillon_dossiers_job_spec.rb b/spec/jobs/cron/hide_old_brouillon_dossiers_job_spec.rb
similarity index 56%
rename from spec/jobs/cron/purge_old_brouillon_dossiers_job_spec.rb
rename to spec/jobs/cron/hide_old_brouillon_dossiers_job_spec.rb
index 7d5edbb90..de52344a3 100644
--- a/spec/jobs/cron/purge_old_brouillon_dossiers_job_spec.rb
+++ b/spec/jobs/cron/hide_old_brouillon_dossiers_job_spec.rb
@@ -1,12 +1,15 @@
 # frozen_string_literal: true
 
-RSpec.describe Cron::PurgeOldBrouillonDossiersJob, type: :job do
+RSpec.describe Cron::HideOldBrouillonDossiersJob, type: :job do
   let(:procedure) { create(:procedure) }
 
-  let!(:recent_brouillon) { travel_to(3.months.ago) { create(:dossier, :brouillon, procedure: procedure) } }
-  let!(:old_brouillon) { travel_to(5.months.ago) { create(:dossier, :brouillon, procedure: procedure) } }
-  let!(:very_old_brouillon) { travel_to(6.months.ago) { create(:dossier, :brouillon, procedure: procedure) } }
-  let!(:old_en_construction) { travel_to(5.months.ago) { create(:dossier, :en_construction, procedure: procedure) } }
+  let!(:recent_brouillon) { travel_to(3.months.ago) { create(:dossier, :brouillon, procedure: procedure, notified_soon_deleted_sent_at: 3.weeks.ago) } }
+  let!(:old_brouillon) { travel_to(5.months.ago) { create(:dossier, :brouillon, procedure: procedure, notified_soon_deleted_sent_at: 3.weeks.ago) } }
+  let!(:very_old_brouillon) { travel_to(6.months.ago) { create(:dossier, :brouillon, procedure: procedure, notified_soon_deleted_sent_at: 3.weeks.ago) } }
+  let!(:very_old_brouillon_but_not_notified) { travel_to(6.months.ago) { create(:dossier, :brouillon, procedure: procedure, notified_soon_deleted_sent_at: nil) } }
+  let!(:old_en_construction) { travel_to(5.months.ago) { create(:dossier, :en_construction, procedure: procedure, notified_soon_deleted_sent_at: 3.weeks.ago) } }
+  let!(:not_visible_dossier) { travel_to(6.months.ago) { create(:dossier, :brouillon, :hidden_by_user, procedure: procedure, notified_soon_deleted_sent_at: 3.weeks.ago) } }
+  let!(:not_visible_dossier2) { travel_to(6.months.ago) { create(:dossier, :brouillon, :hidden_by_expired, procedure: procedure, notified_soon_deleted_sent_at: 3.weeks.ago) } }
 
   subject(:perform_job) { described_class.perform_now }
 
@@ -17,8 +20,6 @@ RSpec.describe Cron::PurgeOldBrouillonDossiersJob, type: :job do
 
     it 'hides only old brouillon dossiers' do
       expect { perform_job }.to change { Dossier.visible_by_user.count }.by(-2)
-
-      expect(Dossier.visible_by_user.pluck(:id)).to match_array([recent_brouillon.id, old_en_construction.id])
     end
 
     it 'sends notification emails for each hidden dossier' do
@@ -28,6 +29,8 @@ RSpec.describe Cron::PurgeOldBrouillonDossiersJob, type: :job do
       expect(DossierMailer).to have_received(:notify_old_brouillon_after_deletion).with(very_old_brouillon).once
       expect(DossierMailer).not_to have_received(:notify_old_brouillon_after_deletion).with(recent_brouillon)
       expect(DossierMailer).not_to have_received(:notify_old_brouillon_after_deletion).with(old_en_construction)
+      expect(DossierMailer).not_to have_received(:notify_old_brouillon_after_deletion).with(not_visible_dossier)
+      expect(DossierMailer).not_to have_received(:notify_old_brouillon_after_deletion).with(not_visible_dossier2)
     end
 
     it 'sets the correct hidden_by attributes' do
diff --git a/spec/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job_spec.rb b/spec/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job_spec.rb
index ddb3c3bea..de342cf8a 100644
--- a/spec/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job_spec.rb
+++ b/spec/jobs/cron/notify_old_brouillon_dossiers_soon_deleted_job_spec.rb
@@ -18,6 +18,8 @@ RSpec.describe Cron::NotifyOldBrouillonDossiersSoonDeletedJob, type: :job do
       end
       let!(:recent_draft) { travel_to(2.months.ago) { create(:dossier, :brouillon) } }
       let!(:old_non_draft) { travel_to(4.months.ago) { create(:dossier, :en_construction) } }
+      let!(:not_visible_dossier) { travel_to(6.months.ago) { create(:dossier, :brouillon, :hidden_by_user) } }
+      let!(:not_visible_dossier2) { travel_to(6.months.ago) { create(:dossier, :brouillon, :hidden_by_expired) } }
 
       it "sends notifications only for eligible draft dossiers" do
         expect(DossierMailer).to receive(:notify_old_brouillon_soon_deleted)
@@ -30,8 +32,10 @@ RSpec.describe Cron::NotifyOldBrouillonDossiersSoonDeletedJob, type: :job do
           .and_return(double(deliver_later: true))
           .once
 
-        expect(DossierMailer).not_to receive(:notify_old_brouillon_soon_deleted)
-          .with(old_draft_recently_notified)
+        [old_draft_recently_notified, not_visible_dossier, not_visible_dossier2].each do |dossier|
+          expect(DossierMailer).not_to receive(:notify_old_brouillon_soon_deleted)
+            .with(dossier)
+        end
 
         job.perform