diff --git a/loopy/codegen/loop.py b/loopy/codegen/loop.py
index b3a87798840bb1624d350c79830f29142e54ab6c..bc013307fc88b16c160b0f91897581c3658691b3 100644
--- a/loopy/codegen/loop.py
+++ b/loopy/codegen/loop.py
@@ -80,11 +80,16 @@ def get_slab_decomposition(kernel, iname):
 
         if upper_incr:
             assert upper_incr > 0
-            upper_slab = ("final", isl.BasicSet.universe(space)
-                    .add_constraint(
-                        isl.Constraint.inequality_from_aff(
-                            iname_rel_aff(space,
-                                iname, ">", upper_bound_aff-upper_incr))))
+            upper_bset = isl.BasicSet.universe(space).add_constraint(
+                isl.Constraint.inequality_from_aff(
+                    iname_rel_aff(space,
+                        iname, ">", upper_bound_aff-upper_incr)))
+            if lower_incr:
+                # Ensure that this slab is actually distinct from the
+                # lower one, if it exists.
+                _, lower_bset = lower_slab
+                upper_bset, = upper_bset.subtract(lower_bset).get_basic_sets()
+            upper_slab = ("final", upper_bset)
             upper_bulk_bound = (
                     isl.Constraint.inequality_from_aff(
                         iname_rel_aff(space,
diff --git a/test/test_split_iname_slabs.py b/test/test_split_iname_slabs.py
new file mode 100644
index 0000000000000000000000000000000000000000..47f311ab583eda037f7798c5c67361e2d8f2828b
--- /dev/null
+++ b/test/test_split_iname_slabs.py
@@ -0,0 +1,66 @@
+__copyright__ = "Copyright (C) 2020 Lawrence Mitchell"
+
+__license__ = """
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+"""
+import loopy as lp
+import numpy as np
+import pyopencl as cl  # noqa
+import pyopencl.array as clarray
+import pytest
+from loopy.version import LOOPY_USE_LANGUAGE_VERSION_2018_2  # noqa
+from pyopencl.tools import \
+    pytest_generate_tests_for_pyopencl as pytest_generate_tests  # noqa
+
+
+@pytest.fixture
+def vanilla():
+    k = lp.make_kernel("{ [i] : k <= i < n}",
+                       """
+                       a[i] = a[i] + 1
+                       """,
+                       [lp.ValueArg("k", dtype="int32"),
+                        lp.ValueArg("n", dtype="int32"),
+                        lp.GlobalArg("a", shape=(None, ),
+                                        dtype="int32")])
+    k = lp.assume(k, "k >= 0 and n >= k")
+    return k
+
+
+@pytest.fixture
+def split(vanilla):
+    k = lp.split_iname(vanilla, "i", 4, slabs=(1, 1))
+    k = lp.prioritize_loops(k, "i_outer,i_inner")
+    return k
+
+
+@pytest.fixture(params=[(1, 4), (1, 5), (4, 8)],
+                ids=lambda x: "{k=%s, n=%s}" % x)
+def parameters(request):
+    return dict(zip("kn", request.param))
+
+
+def test_split_slabs(ctx_factory, vanilla, split, parameters):
+    ctx = ctx_factory()
+    queue = cl.CommandQueue(ctx)
+    expect = clarray.zeros(queue, 8, dtype=np.int32)
+    actual = clarray.zeros(queue, 8, dtype=np.int32)
+    _, (expect, ) = vanilla(queue, a=expect, **parameters)
+    _, (actual, ) = split(queue, a=actual, **parameters)
+    assert np.array_equal(expect.get(), actual.get())