diff --git a/tensorflow_probability/python/experimental/autobnn/bnn_tree.py b/tensorflow_probability/python/experimental/autobnn/bnn_tree.py
index 18e7dacaf2..4e63635d2a 100644
--- a/tensorflow_probability/python/experimental/autobnn/bnn_tree.py
+++ b/tensorflow_probability/python/experimental/autobnn/bnn_tree.py
@@ -27,16 +27,15 @@
 Array = jnp.ndarray
 
 
-LEAVES = [
+NON_PERIODIC_KERNELS = [
     kernels.ExponentiatedQuadraticBNN,
-    kernels.MaternBNN,
-    kernels.ExponentialBNN,
     kernels.LinearBNN,
     kernels.QuadraticBNN,
-    kernels.PeriodicBNN,
-    kernels.OneLayerBNN,
+    # Don't use Matern, Exponential or OneLayer BNN's in the leaves because
+    # they all give very similar predictions to ExponentiatedQuadratic.
 ]
 
+LEAVES = NON_PERIODIC_KERNELS + [kernels.PeriodicBNN]
 
 OPERATORS = [
     operators.Multiply,
@@ -47,16 +46,6 @@
 ]
 
 
-NON_PERIODIC_KERNELS = [
-    kernels.ExponentiatedQuadraticBNN,
-    kernels.MaternBNN,
-    kernels.ExponentialBNN,
-    kernels.LinearBNN,
-    kernels.QuadraticBNN,
-    kernels.OneLayerBNN,
-]
-
-
 def list_of_all(
     time_series_xs: Array,
     depth: int = 2,
diff --git a/tensorflow_probability/python/experimental/autobnn/bnn_tree_test.py b/tensorflow_probability/python/experimental/autobnn/bnn_tree_test.py
index 67e6f87334..197c535dbe 100644
--- a/tensorflow_probability/python/experimental/autobnn/bnn_tree_test.py
+++ b/tensorflow_probability/python/experimental/autobnn/bnn_tree_test.py
@@ -27,23 +27,24 @@ class TreeTest(parameterized.TestCase):
 
   def test_list_of_all_depth0(self):
     l0 = bnn_tree.list_of_all(jnp.linspace(0.0, 100.0, 100), 0)
-    # With no periods, there should be six kernels.
-    self.assertLen(l0, 6)
+    # With no periods, there should be three kernels.
+    self.assertLen(l0, 3)
     for k in l0:
       self.assertFalse(k.going_to_be_multiplied)
 
     l0 = bnn_tree.list_of_all(100, 0, 50, [20.0, 40.0], parent_is_multiply=True)
-    self.assertLen(l0, 8)
+    # With two periods specified, 3+2 = 5.
+    self.assertLen(l0, 5)
     for k in l0:
       self.assertTrue(k.going_to_be_multiplied)
 
   def test_list_of_all_depth1(self):
     l1 = bnn_tree.list_of_all(jnp.linspace(0.0, 100.0, 100), 1)
     # With no periods, there should be
-    # choose(6+1, 2) = 21 trees with a Multiply top node,
-    # choose(6, 2) = 15 trees with a WeightedSum top node, and
-    # 6*6 = 36 trees with a LearnableChangePoint top node.
-    self.assertLen(l1, 72)
+    # choose(3+1, 2) = 6 trees with a Multiply top node,
+    # choose(3, 2) = 3 trees with a WeightedSum top node, and
+    # 3*3 = 9 trees with a LearnableChangePoint top node.
+    self.assertLen(l1, 18)
 
     # Check that all of the BNNs in the tree can be trained.
     for k in l1:
@@ -61,16 +62,16 @@ def test_list_of_all_depth1(self):
         parent_is_multiply=True,
     )
     # With 2 periods and parent_is_multiply, there are only WeightedSum top
-    # nodes, with 7*8/2 = 28 trees.
-    self.assertLen(l1, 28)
+    # nodes, with 4*5/2 = 10 trees.
+    self.assertLen(l1, 10)
 
   def test_list_of_all_depth2(self):
     l2 = bnn_tree.list_of_all(jnp.linspace(0.0, 100.0, 100), 2)
-    # There are 66 trees of depth 1, of which 15 are safe to multiply.
-    # choose(15+1, 2) = 120 trees with a Multiply top node,
-    # choose(66, 2) = 2145 trees with a WeightedSum top node, and
-    # 66*66 = 4356 trees with a LearnableChangePoint top node.
-    self.assertLen(l2, 7860)
+    # There are 18 trees of depth 1, of which 3 are safe to multiply.
+    # choose(3+1, 2) = 6 trees with a Multiply top node,
+    # choose(18, 2) = 153 trees with a WeightedSum top node, and
+    # 18*18 = 324 trees with a LearnableChangePoint top node.
+    self.assertLen(l2, 483)
 
   @parameterized.parameters(0, 1)  # depth=2 segfaults on my desktop :(
   def test_weighted_sum_of_all(self, depth):