diff --git a/doc/whats-new.rst b/doc/whats-new.rst
index 677b2194a55..26c889d241e 100644
--- a/doc/whats-new.rst
+++ b/doc/whats-new.rst
@@ -33,7 +33,8 @@ Deprecations
 
 Bug Fixes
 ~~~~~~~~~
-
+- Always normalize slices when indexing ``LazilyIndexedArray`` instances (:issue:`10941`, :pull:`10948`).
+  By `Justus Magin <https://github.com/keewis>`_.
 
 Documentation
 ~~~~~~~~~~~~~
diff --git a/xarray/core/indexing.py b/xarray/core/indexing.py
index 5d022d0430b..2a86afc0a98 100644
--- a/xarray/core/indexing.py
+++ b/xarray/core/indexing.py
@@ -355,6 +355,17 @@ def slice_slice_by_array(
     return new_indexer
 
 
+def normalize_indexer(indexer, size):
+    if isinstance(indexer, slice):
+        return normalize_slice(indexer, size)
+    elif isinstance(indexer, np.ndarray):
+        return normalize_array(indexer, size)
+    else:
+        if indexer < 0:
+            return size + indexer
+        return indexer
+
+
 def _index_indexer_1d(
     old_indexer: OuterIndexerType,
     applied_indexer: OuterIndexerType,
@@ -365,7 +376,7 @@ def _index_indexer_1d(
         return old_indexer
     if is_full_slice(old_indexer):
         # shortcut for full slices
-        return applied_indexer
+        return normalize_indexer(applied_indexer, size)
 
     indexer: OuterIndexerType
     if isinstance(old_indexer, slice):
diff --git a/xarray/tests/test_indexing.py b/xarray/tests/test_indexing.py
index ffcfd3116f4..6b564c6f032 100644
--- a/xarray/tests/test_indexing.py
+++ b/xarray/tests/test_indexing.py
@@ -275,6 +275,24 @@ def test_read_only_view(self) -> None:
 
 
 class TestLazyArray:
+    @pytest.mark.parametrize(
+        ["indexer", "size", "expected"],
+        (
+            (4, 5, 4),
+            (-1, 3, 2),
+            (slice(None), 4, slice(0, 4, 1)),
+            (slice(1, -3), 7, slice(1, 4, 1)),
+            (np.array([-1, 3, -2]), 5, np.array([4, 3, 3])),
+        ),
+    )
+    def normalize_indexer(self, indexer, size, expected):
+        actual = indexing.normalize_indexer(indexer, size)
+
+        if isinstance(expected, np.ndarray):
+            np.testing.assert_equal(actual, expected)
+        else:
+            assert actual == expected
+
     def test_slice_slice(self) -> None:
         arr = ReturnItem()
         for size in [100, 99]:
@@ -321,6 +339,47 @@ def test_slice_slice_by_array(self, old_slice, array, size):
         expected = np.arange(size)[old_slice][array]
         assert_array_equal(actual, expected)
 
+    @pytest.mark.parametrize(
+        ["old_indexer", "indexer", "size", "expected"],
+        (
+            pytest.param(
+                slice(None), slice(None, 3), 5, slice(0, 3, 1), id="full_slice-slice"
+            ),
+            pytest.param(
+                slice(None), np.arange(2, 4), 5, np.arange(2, 4), id="full_slice-array"
+            ),
+            pytest.param(slice(None), 3, 5, 3, id="full_slice-int"),
+            pytest.param(
+                slice(2, 12, 3), slice(1, 3), 16, slice(5, 11, 3), id="slice_step-slice"
+            ),
+            pytest.param(
+                slice(2, 12, 3),
+                np.array([1, 3]),
+                16,
+                np.array([5, 11]),
+                id="slice_step-array",
+            ),
+            pytest.param(
+                np.arange(5), slice(1, 3), 7, np.arange(1, 3), id="array-slice"
+            ),
+            pytest.param(
+                np.arange(0, 8, 2),
+                np.arange(1, 3),
+                9,
+                np.arange(2, 6, 2),
+                id="array-array",
+            ),
+            pytest.param(np.arange(3), 2, 5, 2, id="array-int"),
+        ),
+    )
+    def test_index_indexer_1d(self, old_indexer, indexer, size, expected):
+        actual = indexing._index_indexer_1d(old_indexer, indexer, size)
+
+        if isinstance(expected, np.ndarray):
+            np.testing.assert_equal(actual, expected)
+        else:
+            assert actual == expected
+
     def test_lazily_indexed_array(self) -> None:
         original = np.random.rand(10, 20, 30)
         x = indexing.NumpyIndexingAdapter(original)