diff --git a/app/services/piece_justificative_to_champ_piece_jointe_migration_service.rb b/app/services/piece_justificative_to_champ_piece_jointe_migration_service.rb
index 0778454f3..52314b697 100644
--- a/app/services/piece_justificative_to_champ_piece_jointe_migration_service.rb
+++ b/app/services/piece_justificative_to_champ_piece_jointe_migration_service.rb
@@ -9,6 +9,11 @@ class PieceJustificativeToChampPieceJointeMigrationService
     storage_service.ensure_openstack_copy_possible!(PieceJustificativeUploader)
   end
 
+  def procedures_with_pjs_in_range(ids_range)
+    procedures_with_pj = Procedure.unscope(where: :hidden_at).joins(:types_de_piece_justificative).distinct
+    procedures_with_pj.where(id: ids_range)
+  end
+
   def convert_procedure_pjs_to_champ_pjs(procedure)
     types_de_champ_pj = PiecesJustificativesService.types_pj_as_types_de_champ(procedure)
     populate_champs_pjs!(procedure, types_de_champ_pj)
diff --git a/lib/tasks/2019_03_13_migrate_pjs_to_champs.rake b/lib/tasks/2019_03_13_migrate_pjs_to_champs.rake
deleted file mode 100644
index ad8194116..000000000
--- a/lib/tasks/2019_03_13_migrate_pjs_to_champs.rake
+++ /dev/null
@@ -1,8 +0,0 @@
-namespace :'2019_03_13_migrate_pjs_to_champs' do
-  task run: :environment do
-    procedure_id = ENV['PROCEDURE_ID']
-    service = PieceJustificativeToChampPieceJointeMigrationService.new
-    service.ensure_correct_storage_configuration!
-    service.convert_procedure_pjs_to_champ_pjs(Procedure.find(procedure_id))
-  end
-end
diff --git a/lib/tasks/pieces_justificatives.rake b/lib/tasks/pieces_justificatives.rake
new file mode 100644
index 000000000..a30855090
--- /dev/null
+++ b/lib/tasks/pieces_justificatives.rake
@@ -0,0 +1,28 @@
+require Rails.root.join("lib", "tasks", "task_helper")
+
+namespace :pieces_justificatives do
+  task migrate_procedure_to_champs: :environment do
+    procedure_id = ENV['PROCEDURE_ID']
+    service = PieceJustificativeToChampPieceJointeMigrationService.new
+    service.ensure_correct_storage_configuration!
+    service.convert_procedure_pjs_to_champ_pjs(Procedure.find(procedure_id))
+  end
+
+  task migrate_procedures_range_to_champs: :environment do
+    if ENV['RANGE_START'].nil? || ENV['RANGE_END'].nil?
+      fail "RANGE_START and RANGE_END must be specified"
+    end
+    procedures_range = ENV['RANGE_START']..ENV['RANGE_END']
+
+    service = PieceJustificativeToChampPieceJointeMigrationService.new
+    service.ensure_correct_storage_configuration!
+    procedures_to_migrate = service.procedures_with_pjs_in_range(procedures_range)
+
+    procedures_to_migrate.find_each do |procedure|
+      rake_puts ''
+      rake_puts "Migrating procedure #{procedure.id}…"
+
+      service.convert_procedure_pjs_to_champ_pjs(procedure)
+    end
+  end
+end
diff --git a/spec/lib/tasks/pieces_justificatives_spec.rb b/spec/lib/tasks/pieces_justificatives_spec.rb
new file mode 100644
index 000000000..5031c772d
--- /dev/null
+++ b/spec/lib/tasks/pieces_justificatives_spec.rb
@@ -0,0 +1,32 @@
+describe 'pieces_justificatives' do
+  describe 'migrate_procedures_range_to_champs' do
+    let(:rake_task) { Rake::Task['pieces_justificatives:migrate_procedures_range_to_champs'] }
+    let(:procedure_in_range_1) { create(:procedure, :with_two_type_de_piece_justificative) }
+    let(:procedure_in_range_2) { create(:procedure, :with_two_type_de_piece_justificative) }
+    let(:procedure_out_of_range) { create(:procedure, :with_two_type_de_piece_justificative) }
+
+    before do
+      procedure_in_range_1
+      procedure_in_range_2
+      procedure_out_of_range
+
+      ENV['RANGE_START'] = procedure_in_range_1.id.to_s
+      ENV['RANGE_END'] = procedure_in_range_2.id.to_s
+
+      allow_any_instance_of(PieceJustificativeToChampPieceJointeMigrationService).to receive(:ensure_correct_storage_configuration!)
+
+      rake_task.invoke
+    end
+
+    after { rake_task.reenable }
+
+    it 'migrates procedures in the ids range' do
+      expect(procedure_in_range_1.reload.types_de_piece_justificative).to be_empty
+      expect(procedure_in_range_2.reload.types_de_piece_justificative).to be_empty
+    end
+
+    it 'doesn’t migrate procedures not in the range' do
+      expect(procedure_out_of_range.reload.types_de_piece_justificative).to be_present
+    end
+  end
+end