diff --git a/app/models/institution_subject.rb b/app/models/institution_subject.rb
index 0f23adc8e0..f7c27df4bc 100644
--- a/app/models/institution_subject.rb
+++ b/app/models/institution_subject.rb
@@ -13,6 +13,7 @@
 #
 #  index_institutions_subjects_on_institution_id  (institution_id)
 #  index_institutions_subjects_on_subject_id      (subject_id)
+#  unique_institution_subject_in_institution      (subject_id,institution_id,description) UNIQUE
 #
 # Foreign Keys
 #
@@ -36,6 +37,18 @@ class InstitutionSubject < ApplicationRecord
   has_many :experts, through: :experts_subjects, inverse_of: :institutions_subjects
   has_many :not_deleted_experts, through: :experts_subjects, inverse_of: :institutions_subjects
 
+  # :institution
+  # Other InstitutionSubjects of the same Institution, and the same Subject.
+  has_many :similar_institutions_subjects, -> (is) { where(subject: is.subject).where.not(id: is.id) },
+           through: :institution, source: :institutions_subjects, inverse_of: :similar_institutions_subjects
+
+  # Validations
+  #
+  # In an Institution, the same subject can only be selected several times`
+  # if the description is different (and present.)
+  validates :subject, uniqueness: { scope: [:institution_id, :description] }
+  validate :validate_description_presence
+
   ## Scopes
   #
   scope :support_subjects, -> do
@@ -53,6 +66,15 @@ def to_s
     description
   end
 
+  ## Name / Description uniqueness
+  #
+  def validate_description_presence
+    # description mustn't be blank if there’s a similar subject
+    if description.blank? && similar_institutions_subjects.present?
+      errors.add(:description, :blank)
+    end
+  end
+
   ## used for serialization in advisors csv
   #
   def csv_identifier
diff --git a/app/models/subject.rb b/app/models/subject.rb
index deafc03667..ea4f5a326c 100644
--- a/app/models/subject.rb
+++ b/app/models/subject.rb
@@ -15,6 +15,7 @@
 # Indexes
 #
 #  index_subjects_on_archived_at  (archived_at)
+#  index_subjects_on_label        (label) UNIQUE
 #  index_subjects_on_slug         (slug) UNIQUE
 #  index_subjects_on_theme_id     (theme_id)
 #
@@ -38,6 +39,7 @@ class Subject < ApplicationRecord
   ## Validations
   #
   validates :theme, :slug, presence: true
+  validates :label, presence: true, uniqueness: true
   before_validation :compute_slug
   before_save :set_support
 
diff --git a/db/migrate/20201002163301_make_subject_label_unique.rb b/db/migrate/20201002163301_make_subject_label_unique.rb
new file mode 100644
index 0000000000..f4ab4c646b
--- /dev/null
+++ b/db/migrate/20201002163301_make_subject_label_unique.rb
@@ -0,0 +1,6 @@
+class MakeSubjectLabelUnique < ActiveRecord::Migration[6.0]
+  def change
+    add_index :subjects, :label, unique: true
+    add_index :institutions_subjects, [:subject_id, :institution_id, :description], unique: true, name: 'unique_institution_subject_in_institution'
+  end
+end
diff --git a/db/schema.rb b/db/schema.rb
index 6e720703c2..1a6c004681 100644
--- a/db/schema.rb
+++ b/db/schema.rb
@@ -10,7 +10,7 @@
 #
 # It's strongly recommended that you check this file into your version control system.
 
-ActiveRecord::Schema.define(version: 2020_10_02_071333) do
+ActiveRecord::Schema.define(version: 2020_10_02_163301) do
 
   # These are extensions that must be enabled in order to support this database
   enable_extension "plpgsql"
@@ -243,6 +243,7 @@
     t.datetime "created_at", null: false
     t.datetime "updated_at", null: false
     t.index ["institution_id"], name: "index_institutions_subjects_on_institution_id"
+    t.index ["subject_id", "institution_id", "description"], name: "unique_institution_subject_in_institution", unique: true
     t.index ["subject_id"], name: "index_institutions_subjects_on_subject_id"
   end
 
@@ -370,6 +371,7 @@
     t.boolean "is_support", default: false
     t.string "slug", null: false
     t.index ["archived_at"], name: "index_subjects_on_archived_at"
+    t.index ["label"], name: "index_subjects_on_label", unique: true
     t.index ["slug"], name: "index_subjects_on_slug", unique: true
     t.index ["theme_id"], name: "index_subjects_on_theme_id"
   end
diff --git a/doc/domain_model.pdf b/doc/domain_model.pdf
index 682ca3a625..98b13b131d 100644
Binary files a/doc/domain_model.pdf and b/doc/domain_model.pdf differ
diff --git a/spec/models/institution_subject_spec.rb b/spec/models/institution_subject_spec.rb
index 8b99dc78d1..826b1127a5 100644
--- a/spec/models/institution_subject_spec.rb
+++ b/spec/models/institution_subject_spec.rb
@@ -8,6 +8,45 @@
       is_expected.to belong_to :subject
       is_expected.to belong_to :institution
     end
+
+    describe 'description uniqueness in an institution' do
+      let(:institution) { create :institution }
+      let(:the_subject) { create :subject }
+
+      before do
+        create :institution_subject, institution: institution, subject: the_subject, description: 'FOO'
+      end
+
+      context 'same institution and subject and description' do
+        subject { build :institution_subject, institution: institution, subject: the_subject, description: 'FOO' }
+
+        it { is_expected.not_to be_valid }
+      end
+
+      context 'same institution and subject, no description' do
+        subject { build :institution_subject, institution: institution, subject: the_subject, description: '' }
+
+        it { is_expected.not_to be_valid }
+      end
+
+      context 'same institution and subject, differetn description' do
+        subject { build :institution_subject, institution: institution, subject: the_subject, description: 'BAR' }
+
+        it { is_expected.to be_valid }
+      end
+
+      context 'same institution, other subject' do
+        subject { build :institution_subject, institution: institution }
+
+        it { is_expected.to be_valid }
+      end
+
+      context 'other institution, same subject' do
+        subject { build :institution_subject, subject: the_subject }
+
+        it { is_expected.to be_valid }
+      end
+    end
   end
 
   describe 'csv_identifier' do