diff --git a/numcodecs/delta.py b/numcodecs/delta.py
index f6307312..a76ce483 100644
--- a/numcodecs/delta.py
+++ b/numcodecs/delta.py
@@ -67,7 +67,7 @@ def encode(self, buf):
         if arr.dtype == bool:
             np.not_equal(arr[1:], arr[:-1], out=enc[1:])
         else:
-            np.subtract(arr[1:], arr[:-1], out=enc[1:])
+            np.subtract(arr[1:], arr[:-1], out=enc[1:], casting='unsafe')
 
         return enc
 
diff --git a/numcodecs/tests/test_delta.py b/numcodecs/tests/test_delta.py
index 9664efee..21c49988 100644
--- a/numcodecs/tests/test_delta.py
+++ b/numcodecs/tests/test_delta.py
@@ -13,19 +13,24 @@
 # mix of dtypes: integer, float
 # mix of shapes: 1D, 2D, 3D
 # mix of orders: C, F
+# mix of encoding types: All available types for each arrays
 arrays = [
-    np.random.randint(0, 1, size=110, dtype='?').reshape(10, 11),
-    np.arange(1000, dtype='<i4'),
-    np.linspace(1000, 1001, 1000, dtype='<f4').reshape(100, 10),
-    np.random.normal(loc=1000, scale=1, size=(10, 10, 10)).astype('<f8'),
-    np.random.randint(0, 200, size=1000, dtype='u2').astype('<u2').reshape(100, 10, order='F'),
+    (np.random.randint(0, 1, size=110, dtype='?').reshape(10, 11), ('?', '<u1', '<i1')),
+    (np.arange(1000, dtype='<i4'), ('<i4', '<i2', '<u4', 'u2')),
+    (np.linspace(1000, 1001, 1000, dtype='<f4').reshape(100, 10), ('<f4',)),
+    (np.random.normal(loc=1000, scale=1, size=(10, 10, 10)).astype('<f8'), ('<f8',)),
+    (
+        np.random.randint(0, 200, size=1000, dtype='u2').astype('<u2').reshape(100, 10, order='F'),
+        ('<i2',),
+    ),
 ]
 
 
 def test_encode_decode():
-    for arr in arrays:
-        codec = Delta(dtype=arr.dtype)
-        check_encode_decode(arr, codec)
+    for arr, encoding_types in arrays:
+        for astype in encoding_types:
+            codec = Delta(dtype=arr.dtype, astype=astype)
+            check_encode_decode(arr, codec)
 
 
 def test_encode():
@@ -49,7 +54,7 @@ def test_repr():
 
 
 def test_backwards_compatibility():
-    for arr in arrays:
+    for arr, _ in arrays:
         codec = Delta(dtype=arr.dtype)
         check_backwards_compatibility(Delta.codec_id, [arr], [codec], prefix=str(arr.dtype))
 
@@ -59,3 +64,35 @@ def test_errors():
         Delta(dtype=object)
     with pytest.raises(ValueError):
         Delta(dtype='i8', astype=object)
+
+
+# overflow tests
+# Note: Before implementing similar test for integer -> integer types, check numpy/numpy#8987.
+oveflow_proned_float_float_pairs = [
+    ('f4', 'f2'),
+    ('f8', 'f4'),
+]
+
+
+def test_oveflow_proned_float_float_encode():
+    for dtype, astype in oveflow_proned_float_float_pairs:
+        codec = Delta(dtype=dtype, astype=astype)
+        arr = np.array([0, np.finfo(astype).max.astype(dtype) * 2], dtype=dtype)
+        with pytest.warns(RuntimeWarning, match=r"overflow encountered"):
+            codec.encode(arr)
+
+
+overflow_proned_integer_float_paris = [
+    ('i4', 'f2'),
+    ('i8', 'f2'),
+    ('u4', 'f2'),
+    ('u8', 'f2'),
+]
+
+
+def test_oveflow_proned_integer_float_encode():
+    for dtype, astype in overflow_proned_integer_float_paris:
+        codec = Delta(dtype=dtype, astype=astype)
+        arr = np.array([0, int(np.rint(np.finfo(astype).max)) * 2], dtype=dtype)
+        with pytest.warns(RuntimeWarning, match=r"overflow encountered"):
+            codec.encode(arr)