diff --git a/src/orion/algo/asha.py b/src/orion/algo/asha.py
index 163c98882..1e7b274e0 100644
--- a/src/orion/algo/asha.py
+++ b/src/orion/algo/asha.py
@@ -232,9 +232,12 @@ def get_candidates(self, rung_id):
 
         rung = list(
             sorted(
-                (objective, trial)
-                for objective, trial in rung.values()
-                if objective is not None
+                (
+                    (objective, trial)
+                    for objective, trial in rung.values()
+                    if objective is not None
+                ),
+                key=lambda item: item[0],
             )
         )
         k = len(rung) // self.hyperband.reduction_factor
diff --git a/src/orion/algo/hyperband.py b/src/orion/algo/hyperband.py
index 39ee75010..dbc3cdc92 100644
--- a/src/orion/algo/hyperband.py
+++ b/src/orion/algo/hyperband.py
@@ -341,7 +341,8 @@ def suggest(self, num):
             )
         else:
             logger.warning(
-                f"{self.__class__.__name__} cannot suggest new samples, exit."
+                f"{self.__class__.__name__} cannot suggest new samples and must wait "
+                "for trials to complete."
             )
 
         return []
diff --git a/tests/unittests/algo/test_asha.py b/tests/unittests/algo/test_asha.py
index 74ec08ecf..f86dec829 100644
--- a/tests/unittests/algo/test_asha.py
+++ b/tests/unittests/algo/test_asha.py
@@ -574,6 +574,36 @@ def test_suggest_promote_many_plus_random(
             == 20 - 2 - 3 * 3
         )
 
+    def test_suggest_promote_identic_objectives(
+        self, asha, bracket, big_rung_0, big_rung_1
+    ):
+        """Test that identic objectives are handled properly"""
+        asha.brackets = [bracket]
+        bracket.asha = asha
+
+        n_trials = 9
+        resources = 1
+
+        results = {}
+        for param in np.linspace(0, 8, 9):
+            trial = create_trial_for_hb((resources, param), objective=0)
+            trial_hash = trial.compute_trial_hash(
+                trial,
+                ignore_fidelity=True,
+                ignore_experiment=True,
+            )
+            results[trial_hash] = (trial.objective.value, trial)
+
+        bracket.rungs[0] = dict(n_trials=n_trials, resources=resources, results=results)
+
+        candidates = asha.suggest(2)
+
+        assert len(candidates) == 2
+        assert (
+            sum(1 for trial in candidates if trial.params[asha.fidelity_index] == 3)
+            == 2
+        )
+
 
 class TestGenericASHA(BaseAlgoTests):
     algo_name = "asha"
diff --git a/tests/unittests/algo/test_hyperband.py b/tests/unittests/algo/test_hyperband.py
index dad44b9b8..58da7da18 100644
--- a/tests/unittests/algo/test_hyperband.py
+++ b/tests/unittests/algo/test_hyperband.py
@@ -584,6 +584,36 @@ def test_suggest_promote(self, hyperband, bracket, rung_0):
         assert points[1].params == {"epoch": 3, "lr": 1}
         assert points[2].params == {"epoch": 3, "lr": 2}
 
+    def test_suggest_promote_identic_objectives(self, hyperband, bracket):
+        """Test that identic objectives are handled properly"""
+        hyperband.brackets = [bracket]
+        bracket.hyperband = hyperband
+
+        n_trials = 9
+        resources = 1
+
+        results = {}
+        for param in np.linspace(0, 8, 9):
+            trial = create_trial_for_hb((resources, param), objective=0)
+            trial_hash = trial.compute_trial_hash(
+                trial,
+                ignore_fidelity=True,
+                ignore_experiment=True,
+            )
+            results[trial_hash] = (trial.objective.value, trial)
+
+        bracket.rungs[0] = dict(n_trials=n_trials, resources=resources, results=results)
+
+        candidates = hyperband.suggest(2)
+
+        assert len(candidates) == 2
+        assert (
+            sum(
+                1 for trial in candidates if trial.params[hyperband.fidelity_index] == 3
+            )
+            == 2
+        )
+
     def test_is_filled(self, hyperband, bracket, rung_0, rung_1, rung_2):
         """Test that Hyperband bracket detects when rung is filled."""
         hyperband.brackets = [bracket]