diff --git a/app/models/ci/pipeline.rb b/app/models/ci/pipeline.rb
index 3cdb86e7b55eb83b28c213c00ca8d4b301df634b..efab6f4283ac0c82b83f8a23f5556dc95d6612f3 100644
--- a/app/models/ci/pipeline.rb
+++ b/app/models/ci/pipeline.rb
@@ -14,7 +14,7 @@ module Ci
     belongs_to :auto_canceled_by, class_name: 'Ci::Pipeline'
     belongs_to :pipeline_schedule, class_name: 'Ci::PipelineSchedule'
 
-    has_internal_id :iid_per_project, scope: :project, init: ->(s) { s&.project&.pipelines.count }
+    has_internal_id :iid, scope: :project, init: ->(s) { s&.project&.pipelines.count }
 
     has_many :stages
     has_many :statuses, class_name: 'CommitStatus', foreign_key: :commit_id, inverse_of: :pipeline
@@ -492,7 +492,7 @@ module Ci
     def predefined_variables
       Gitlab::Ci::Variables::Collection.new
         .append(key: 'CI_PIPELINE_ID', value: id.to_s)
-        .append(key: 'CI_PIPELINE_IID_PER_PROJECT', value: iid_per_project.to_s)
+        .append(key: 'CI_PIPELINE_IID_PER_PROJECT', value: iid.to_s)
         .append(key: 'CI_CONFIG_PATH', value: ci_yaml_file_path)
         .append(key: 'CI_PIPELINE_SOURCE', value: source.to_s)
     end
diff --git a/db/migrate/20180424160449_add_pipeline_iid_to_ci_pipelines.rb b/db/migrate/20180424160449_add_pipeline_iid_to_ci_pipelines.rb
index 128377e1c9d3ecdb4abf339d5fd5c0b693e01df6..d732116e9ce9858964693e0f6c2e3948c6ef08f2 100644
--- a/db/migrate/20180424160449_add_pipeline_iid_to_ci_pipelines.rb
+++ b/db/migrate/20180424160449_add_pipeline_iid_to_ci_pipelines.rb
@@ -6,10 +6,10 @@ class AddPipelineIidToCiPipelines < ActiveRecord::Migration
   disable_ddl_transaction!
 
   def up
-    add_column :ci_pipelines, :iid_per_project, :integer
+    add_column :ci_pipelines, :iid, :integer
   end
 
   def down
-    remove_column :ci_pipelines, :iid_per_project, :integer
+    remove_column :ci_pipelines, :iid, :integer
   end
 end
diff --git a/db/migrate/20180425205249_add_index_constraints_to_pipeline_iid.rb b/db/migrate/20180425205249_add_index_constraints_to_pipeline_iid.rb
index 7daa7197b7c3409b1397191b70e4aa7f4fbdcb14..3fa59b44d5d79014ea5e590af37c79b05c7e6403 100644
--- a/db/migrate/20180425205249_add_index_constraints_to_pipeline_iid.rb
+++ b/db/migrate/20180425205249_add_index_constraints_to_pipeline_iid.rb
@@ -6,10 +6,10 @@ class AddIndexConstraintsToPipelineIid < ActiveRecord::Migration
   disable_ddl_transaction!
 
   def up
-    add_concurrent_index :ci_pipelines, [:project_id, :iid_per_project], unique: true, where: 'iid_per_project IS NOT NULL'
+    add_concurrent_index :ci_pipelines, [:project_id, :iid], unique: true, where: 'iid IS NOT NULL'
   end
 
   def down
-    remove_concurrent_index :ci_pipelines, [:project_id, :iid_per_project]
+    remove_concurrent_index :ci_pipelines, [:project_id, :iid]
   end
 end
diff --git a/db/schema.rb b/db/schema.rb
index af838e109b2b3c590749054cad56e2183c4915f8..50abe1a883819bce6d28b072e9dd04c2a4c06818 100644
--- a/db/schema.rb
+++ b/db/schema.rb
@@ -434,12 +434,12 @@ ActiveRecord::Schema.define(version: 20180425205249) do
     t.integer "config_source"
     t.boolean "protected"
     t.integer "failure_reason"
-    t.integer "iid_per_project"
+    t.integer "iid"
   end
 
   add_index "ci_pipelines", ["auto_canceled_by_id"], name: "index_ci_pipelines_on_auto_canceled_by_id", using: :btree
   add_index "ci_pipelines", ["pipeline_schedule_id"], name: "index_ci_pipelines_on_pipeline_schedule_id", using: :btree
-  add_index "ci_pipelines", ["project_id", "iid_per_project"], name: "index_ci_pipelines_on_project_id_and_iid_per_project", unique: true, where: "(iid_per_project IS NOT NULL)", using: :btree
+  add_index "ci_pipelines", ["project_id", "iid"], name: "index_ci_pipelines_on_project_id_and_iid", unique: true, where: "(iid IS NOT NULL)", using: :btree
   add_index "ci_pipelines", ["project_id", "ref", "status", "id"], name: "index_ci_pipelines_on_project_id_and_ref_and_status_and_id", using: :btree
   add_index "ci_pipelines", ["project_id", "sha"], name: "index_ci_pipelines_on_project_id_and_sha", using: :btree
   add_index "ci_pipelines", ["project_id"], name: "index_ci_pipelines_on_project_id", using: :btree