diff --git a/pymc3/tests/models.py b/pymc3/tests/models.py
index 78324e72c7c..d9150a27ce3 100644
--- a/pymc3/tests/models.py
+++ b/pymc3/tests/models.py
@@ -215,7 +215,7 @@ def simple_normal(bounded_prior=False):
     sd = 1.0
     a, b = (9, 12)  # bounds for uniform RV, need non-symmetric to reproduce issue
 
-    with pm.Model() as model:
+    with pm.Model(rng_seeder=2482) as model:
         if bounded_prior:
             mu_i = pm.Uniform("mu_i", a, b)
         else:
diff --git a/pymc3/tests/test_tuning.py b/pymc3/tests/test_tuning.py
index 038f65f5646..efae88f4820 100644
--- a/pymc3/tests/test_tuning.py
+++ b/pymc3/tests/test_tuning.py
@@ -18,7 +18,6 @@
 
 from pymc3.step_methods.metropolis import tune
 from pymc3.tests import models
-from pymc3.tests.helpers import select_by_precision
 from pymc3.tuning import find_MAP, scaling
 
 
@@ -37,7 +36,7 @@ def test_guess_scaling():
 def test_mle_jacobian():
     """Test MAP / MLE estimation for distributions with flat priors."""
     truth = 10.0  # Simple normal model should give mu=10.0
-    rtol = select_by_precision(float64=1e-6, float32=1e-4)
+    rtol = 1e-5  # this rtol should work on both floatX precisions
 
     start, model, _ = models.simple_normal(bounded_prior=False)
     with model: