diff --git a/cssselect/xpath.py b/cssselect/xpath.py
index 57b9884..377fc28 100644
--- a/cssselect/xpath.py
+++ b/cssselect/xpath.py
@@ -420,7 +420,7 @@ def xpath_attrib(self, selector: Attrib) -> XPathExpr:
             getattr(self, f"xpath_attrib_{operator}"),
         )
         if self.lower_case_attribute_names:
-            name = selector.attrib.lower()
+            name = ascii_lower(selector.attrib)
         else:
             name = selector.attrib
         if selector.namespace == "*":
@@ -470,7 +470,7 @@ def xpath_element(self, selector: Element) -> XPathExpr:
         else:
             safe = bool(is_safe_name(element))
             if self.lower_case_element_names:
-                element = element.lower()
+                element = ascii_lower(element)
             if selector.namespace == "*":
                 # Namespace wildcard, e.g. "*|div": any namespace,
                 # including none. XPath 1.0 has no "*:name" name test
diff --git a/tests/test_cssselect.py b/tests/test_cssselect.py
index d5d9ec7..4a98eee 100644
--- a/tests/test_cssselect.py
+++ b/tests/test_cssselect.py
@@ -1361,6 +1361,31 @@ def argument_types(css: str) -> list[str]:
             css = f"::pseudo_element({argument_string})"
             assert argument_types(css) == argument_list
 
+    def test_html_non_ascii_element_names(self) -> None:
+        xpath = HTMLTranslator().css_to_xpath
+        assert xpath("x-Ä") == "descendant-or-self::*[name() = 'x-Ä']"
+        assert xpath("X-Ä") == "descendant-or-self::*[name() = 'x-Ä']"
+        assert xpath("*|X-Ä") == "descendant-or-self::*[local-name() = 'x-Ä']"
+        assert xpath("X-ä") == "descendant-or-self::*[name() = 'x-ä']"
+
+    def test_html_non_ascii_attribute_names(self) -> None:
+        xpath = HTMLTranslator().css_to_xpath
+        assert (
+            xpath("[DATA-Ä]")
+            == "descendant-or-self::*[attribute::*[name() = 'data-Ä']]"
+        )
+        assert (
+            xpath('[DATA-Ä="yes"]')
+            == "descendant-or-self::*[attribute::*[name() = 'data-Ä'] = 'yes']"
+        )
+        assert xpath("[*|DATA-Ä]") == (
+            "descendant-or-self::*[attribute::*[local-name() = 'data-Ä']]"
+        )
+        assert (
+            xpath('[DATA-ä="yes"]')
+            == "descendant-or-self::*[attribute::*[name() = 'data-ä'] = 'yes']"
+        )
+
     def test_select(self) -> None:
         document = etree.fromstring(HTML_IDS)
         sort_key = {el: count for count, el in enumerate(document.iter())}.__getitem__