diff --git a/tests/rc/models/bidaf_test.py b/tests/rc/models/bidaf_test.py
index 6095b04d1..9bb14a289 100644
--- a/tests/rc/models/bidaf_test.py
+++ b/tests/rc/models/bidaf_test.py
@@ -20,8 +20,15 @@ class BidirectionalAttentionFlowTest(ModelTestCase):
     def setup_method(self):
         super().setup_method()
         self.set_up_model(
-            FIXTURES_ROOT / "rc" / "bidaf" / "experiment.json", FIXTURES_ROOT / "rc" / "squad.json"
+            FIXTURES_ROOT / "rc" / "bidaf" / "experiment.json",
+            FIXTURES_ROOT / "rc" / "squad.json",
+            seed=27,
         )
+        torch.use_deterministic_algorithms(True)
+
+    def teardown_method(self):
+        super().teardown_method()
+        torch.use_deterministic_algorithms(False)
 
     @flaky
     def test_forward_pass_runs_correctly(self):
@@ -53,7 +60,11 @@ def test_forward_pass_runs_correctly(self):
     # `masked_softmax`...) have made this _very_ flaky...
     @flaky(max_runs=5)
     def test_model_can_train_save_and_load(self):
-        self.ensure_model_can_train_save_and_load(self.param_file, tolerance=1e-4)
+        self.ensure_model_can_train_save_and_load(
+            self.param_file,
+            tolerance=1e-4,
+            gradients_to_ignore={"_span_start_predictor._module.bias"},
+        )
 
     @flaky
     def test_batch_predictions_are_consistent(self):
diff --git a/tests/rc/models/dialog_qa_test.py b/tests/rc/models/dialog_qa_test.py
index ce1ef3999..771963b6d 100644
--- a/tests/rc/models/dialog_qa_test.py
+++ b/tests/rc/models/dialog_qa_test.py
@@ -1,9 +1,9 @@
 from allennlp.common.testing import ModelTestCase
 from allennlp.data import Batch
-
-from tests import FIXTURES_ROOT
+import torch
 
 import allennlp_models.rc
+from tests import FIXTURES_ROOT
 
 
 class DialogQATest(ModelTestCase):
@@ -12,9 +12,15 @@ def setup_method(self):
         self.set_up_model(
             FIXTURES_ROOT / "rc" / "dialog_qa" / "experiment.json",
             FIXTURES_ROOT / "rc" / "dialog_qa" / "quac_sample.json",
+            seed=42,
         )
         self.batch = Batch(self.instances)
         self.batch.index_instances(self.vocab)
+        torch.use_deterministic_algorithms(True)
+
+    def teardown_method(self):
+        super().teardown_method()
+        torch.use_deterministic_algorithms(False)
 
     def test_forward_pass_runs_correctly(self):
         training_tensors = self.batch.as_tensor_dict()
@@ -23,7 +29,9 @@ def test_forward_pass_runs_correctly(self):
         assert "followup" in output_dict and "yesno" in output_dict
 
     def test_model_can_train_save_and_load(self):
-        self.ensure_model_can_train_save_and_load(self.param_file, tolerance=1e-4)
+        self.ensure_model_can_train_save_and_load(
+            self.param_file, tolerance=1e-4, gradients_to_ignore={"_matrix_attention._bias"}
+        )
 
     def test_batch_predictions_are_consistent(self):
         self.ensure_batch_predictions_are_consistent()