diff --git a/h5py/_errors.pyx b/h5py/_errors.pyx
index 612052fb2..88d996843 100644
--- a/h5py/_errors.pyx
+++ b/h5py/_errors.pyx
@@ -80,6 +80,12 @@ _exact_table = {
     (H5E_FILE, H5E_CANTCONVERT):    ValueError, # Invalid file format
 }
 
+# Further fudge: In some cases, the error numbers we care about are those from
+# the bottom (innermost) error in the stack.
+_bottom_exact_table = {
+    (H5E_DATASPACE, H5E_BADRANGE):  IndexError, # Out of range selection
+}
+
 IF HDF5_VERSION > (1, 12, 0):
     _exact_table[(H5E_DATASET, H5E_CANTCREATE)] = ValueError  # bad param for dataset setup
 
@@ -140,6 +146,8 @@ cdef int set_exception() except -1:
     if H5Ewalk(<hid_t>H5E_DEFAULT, H5E_WALK_DOWNWARD, walk_cb, &err) < 0:
         raise RuntimeError("Failed to walk error stack")
 
+    eclass = _bottom_exact_table.get((err.err.maj_num, err.err.min_num), eclass)
+
     desc_bottom = err.err.desc
     if desc_bottom is NULL:
         raise RuntimeError("Failed to extract bottom-level error description")
diff --git a/h5py/tests/test_dataset.py b/h5py/tests/test_dataset.py
index df99f527a..fde90914a 100644
--- a/h5py/tests/test_dataset.py
+++ b/h5py/tests/test_dataset.py
@@ -1753,6 +1753,11 @@ def test_read_points(writable_file):
     res = ds.points[[(0, 0), (1, 0), (2, 2)]]
     np.testing.assert_array_equal(res, [0, 6, 14])
 
+    with pytest.raises(IndexError):
+        ds.points[[(0, 7)]]
+
+    with pytest.raises(IndexError):
+        ds.points[[(-1, 0)]]
 
 def test_write_points(writable_file):
     ds = writable_file.create_dataset('a', shape=(3, 3))
@@ -1764,6 +1769,12 @@ def test_write_points(writable_file):
         [0, 0, 3],
     ])
 
+    with pytest.raises(IndexError):
+        ds.points[[(0, 4)]] = [4]
+
+    with pytest.raises(IndexError):
+        ds.points[[(-1, 0)]] = [5]
+
 
 class TestCommutative(BaseDataset):
     """