diff --git a/tests/test_properties.py b/tests/test_properties.py
index 71fbeeb839..acecd44810 100644
--- a/tests/test_properties.py
+++ b/tests/test_properties.py
@@ -1,4 +1,3 @@
-import numpy as np
 import pytest
 from numpy.testing import assert_array_equal
 
@@ -8,7 +7,7 @@
 
 import hypothesis.extra.numpy as npst
 import hypothesis.strategies as st
-from hypothesis import given
+from hypothesis import assume, given
 
 from zarr.abc.store import Store
 from zarr.core.metadata import ArrayV2Metadata, ArrayV3Metadata
@@ -57,7 +56,7 @@ def test_basic_indexing(data: st.DataObject) -> None:
     actual = zarray[indexer]
     assert_array_equal(nparray[indexer], actual)
 
-    new_data = np.ones_like(actual)
+    new_data = data.draw(npst.arrays(shape=st.just(actual.shape), dtype=nparray.dtype))
     zarray[indexer] = new_data
     nparray[indexer] = new_data
     assert_array_equal(nparray, zarray[:])
@@ -73,6 +72,12 @@ def test_oindex(data: st.DataObject) -> None:
     actual = zarray.oindex[zindexer]
     assert_array_equal(nparray[npindexer], actual)
 
+    assume(zarray.shards is None)  # GH2834
+    new_data = data.draw(npst.arrays(shape=st.just(actual.shape), dtype=nparray.dtype))
+    nparray[npindexer] = new_data
+    zarray.oindex[zindexer] = new_data
+    assert_array_equal(nparray, zarray[:])
+
 
 @given(data=st.data())
 def test_vindex(data: st.DataObject) -> None:
@@ -88,6 +93,14 @@ def test_vindex(data: st.DataObject) -> None:
     actual = zarray.vindex[indexer]
     assert_array_equal(nparray[indexer], actual)
 
+    # FIXME!
+    # when the indexer is such that a value gets overwritten multiple times,
+    # I think the output depends on chunking.
+    # new_data = data.draw(npst.arrays(shape=st.just(actual.shape), dtype=nparray.dtype))
+    # nparray[indexer] = new_data
+    # zarray.vindex[indexer] = new_data
+    # assert_array_equal(nparray, zarray[:])
+
 
 @given(store=stores, meta=array_metadata())  # type: ignore[misc]
 async def test_roundtrip_array_metadata(