diff --git a/onmt/tests/test_greedy_search.py b/onmt/tests/test_greedy_search.py
index fd4291e506..d645740055 100644
--- a/onmt/tests/test_greedy_search.py
+++ b/onmt/tests/test_greedy_search.py
@@ -46,6 +46,7 @@ def test_doesnt_predict_eos_if_shorter_than_min_len(self):
                 2,
                 3,
                 1,
+                1,
                 batch_sz,
                 GlobalScorerStub(),
                 min_length,
@@ -100,6 +101,7 @@ def test_returns_correct_scores_deterministic(self):
                     2,
                     3,
                     1,
+                    1,
                     batch_sz,
                     GlobalScorerStub(),
                     0,
@@ -186,6 +188,7 @@ def test_returns_correct_scores_non_deterministic(self):
                     2,
                     3,
                     1,
+                    1,
                     batch_sz,
                     GlobalScorerStub(),
                     0,
@@ -297,6 +300,7 @@ def test_returns_correct_scores_non_deterministic_beams(self):
                     2,
                     3,
                     1,
+                    1,
                     batch_sz,
                     GlobalScorerStub(),
                     0,
@@ -374,7 +378,7 @@ def test_returns_correct_scores_non_deterministic_beams(self):
 
                 samp.update_finished()
                 self.assertEqual(
-                    [score for score, _, _ in samp.hypotheses[batch_sz - 1][-1:]],
+                    [score for score, _, _ in samp.hypotheses[batch_sz - 1][:1]],
                     [valid_score_dist_2[0] / temp],
                 )
 
@@ -419,6 +423,7 @@ def test_returns_correct_scores_non_deterministic_topp(self):
                     2,
                     3,
                     1,
+                    1,
                     batch_sz,
                     GlobalScorerStub(),
                     0,
diff --git a/onmt/translate/greedy_search.py b/onmt/translate/greedy_search.py
index 8a5707ffa8..0cc58e4e37 100644
--- a/onmt/translate/greedy_search.py
+++ b/onmt/translate/greedy_search.py
@@ -98,6 +98,8 @@ class GreedySearch(DecodeStrategy):
         eos (int): See base.
         unk (int): See base.
         start (int): See base.
+        n_best (int): Don't stop until at least this many beams have
+            reached EOS.
         batch_size (int): See base.
         global_scorer (onmt.translate.GNMTGlobalScorer): Scorer instance.
         min_length (int): See base.
@@ -123,6 +125,7 @@ def __init__(
         eos,
         unk,
         start,
+        n_best,
         batch_size,
         global_scorer,
         min_length,
@@ -157,6 +160,7 @@ def __init__(
         self.keep_topp = keep_topp
         self.topk_scores = None
         self.beam_size = beam_size
+        self.n_best = n_best
 
     def initialize(
         self, enc_out, src_len, src_map=None, device=None, target_prefix=None
@@ -265,10 +269,14 @@ def update_finished(self):
                 else []
             )
             self.hypotheses[b_orig].append((score, pred, attention))
+            if len(self.hypotheses[b_orig]) >= 2:
+                self.hypotheses[b_orig] = sorted(
+                    self.hypotheses[b_orig], key=lambda x: x[0], reverse=True
+                )
         self.done = self.is_finished.all()
         if self.done:
             for b in range(self.batch_size):
-                best_hyp = sorted(self.hypotheses[b], key=lambda x: x[0], reverse=True)
+                best_hyp = self.hypotheses[b][: self.n_best]
                 for score, pred, attn in best_hyp:
                     self.scores[b].append(score)
                     self.predictions[b].append(pred)
diff --git a/onmt/translate/translator.py b/onmt/translate/translator.py
index be6903bcaf..99a835e1aa 100644
--- a/onmt/translate/translator.py
+++ b/onmt/translate/translator.py
@@ -810,6 +810,7 @@ def translate_batch(self, batch, attn_debug):
                     eos=self._tgt_eos_idx,
                     unk=self._tgt_unk_idx,
                     start=self._tgt_start_with,
+                    n_best=self.n_best,
                     batch_size=len(batch["srclen"]),
                     global_scorer=self.global_scorer,
                     min_length=self.min_length,
@@ -1009,6 +1010,7 @@ def translate_batch(self, batch, attn_debug):
                     eos=self._tgt_eos_idx,
                     unk=self._tgt_unk_idx,
                     start=self._tgt_start_with,
+                    n_best=self.n_best,
                     batch_size=len(batch["srclen"]),
                     global_scorer=self.global_scorer,
                     min_length=self.min_length,