diff --git a/dm_env/discrete_array_bounds_test.py b/dm_env/discrete_array_bounds_test.py
new file mode 100644
index 0000000..98ca0ac
--- /dev/null
+++ b/dm_env/discrete_array_bounds_test.py
@@ -0,0 +1,78 @@
+# pylint: disable=g-bad-file-header
+# Copyright 2019 The dm_env Authors. All Rights Reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#    http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or  implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+# ============================================================================
+"""Checks that DiscreteArray validates integer values rather than dtype order."""
+
+import pickle
+
+from absl.testing import absltest
+from absl.testing import parameterized
+from dm_env import specs
+import numpy as np
+
+_INTEGER_DTYPES = (np.int8, np.uint8, np.int16, np.uint16, np.int32, np.uint32,
+                   np.int64, np.uint64)
+
+
+class DiscreteArrayBoundsTest(parameterized.TestCase):
+
+  @parameterized.product(dtype=_INTEGER_DTYPES, excess=(1, 17))
+  def test_rejects_unrepresentable_maximum(self, dtype, excess):
+    num_values = int(np.iinfo(dtype).max) + 1 + excess
+    message = specs._DTYPE_OVERFLOW.format(np.dtype(dtype), num_values)
+    with self.assertRaisesWithLiteralMatch(ValueError, message):
+      specs.DiscreteArray(num_values, dtype=dtype)
+
+  @parameterized.product(dtype=_INTEGER_DTYPES, full_range=(False, True))
+  def test_representable_endpoints_and_round_trip(self, dtype, full_range):
+    maximum = int(np.iinfo(dtype).max) if full_range else 0
+    spec = specs.DiscreteArray(maximum + 1, dtype=dtype, name='action')
+    self.assertEqual(spec.num_values, maximum + 1)
+    self.assertEqual(int(spec.maximum), maximum)
+    for value in (0, maximum):
+      actual = spec.validate(np.asarray(value, dtype=dtype))
+      self.assertEqual(int(actual), value)
+      self.assertEqual(actual.dtype, np.dtype(dtype))
+    spec.validate(spec.generate_value())
+    restored = pickle.loads(pickle.dumps(spec))
+    self.assertEqual(restored, spec)
+    self.assertEqual(restored.num_values, spec.num_values)
+    self.assertEqual(restored.name, 'action')
+
+  @parameterized.parameters('int8', np.dtype('int8'), np.dtype('>i2'))
+  def test_dtype_objects_and_strings_share_overflow_validation(self, dtype):
+    num_values = int(np.iinfo(dtype).max) + 2
+    with self.assertRaisesWithLiteralMatch(
+        ValueError, specs._DTYPE_OVERFLOW.format(np.dtype(dtype), num_values)):
+      specs.DiscreteArray(num_values, dtype=dtype)
+
+  @parameterized.parameters(np.int32(129), np.uint64(129))
+  def test_numpy_integer_counts_use_the_same_check(self, num_values):
+    with self.assertRaisesWithLiteralMatch(
+        ValueError, specs._DTYPE_OVERFLOW.format(np.dtype('int8'), num_values)):
+      specs.DiscreteArray(num_values, dtype=np.int8)
+
+  def test_replacing_dtype_rejects_a_range_that_no_longer_fits(self):
+    original = specs.DiscreteArray(256, np.uint8)
+    with self.assertRaisesWithLiteralMatch(
+        ValueError, specs._DTYPE_OVERFLOW.format(np.dtype('int8'), 256)):
+      original.replace(dtype=np.int8)
+    self.assertEqual(original.dtype, np.dtype('uint8'))
+    self.assertEqual(int(original.maximum), 255)
+    self.assertEqual(int(original.replace(dtype=np.int16).maximum), 255)
+
+
+if __name__ == '__main__':
+  absltest.main()
diff --git a/dm_env/specs.py b/dm_env/specs.py
index 0dc989a..f64a96c 100644
--- a/dm_env/specs.py
+++ b/dm_env/specs.py
@@ -312,7 +312,7 @@ def __init__(self, num_values, dtype=np.int32, name=None):
     maximum = num_values - 1
     dtype = np.dtype(dtype)
 
-    if np.min_scalar_type(maximum) > dtype:
+    if maximum > np.iinfo(dtype).max:
       raise ValueError(_DTYPE_OVERFLOW.format(dtype, num_values))
 
     super(DiscreteArray, self).__init__(