diff --git a/jedi/inference/syntax_tree.py b/jedi/inference/syntax_tree.py
index f55ab56b..1d8b4e2e 100644
--- a/jedi/inference/syntax_tree.py
+++ b/jedi/inference/syntax_tree.py
@@ -2,6 +2,7 @@
 Functions inferring the syntax tree.
 """
 import copy
+import itertools
 
 from parso.python import tree
 
@@ -515,10 +516,20 @@ def _literals_to_types(inference_state, result):
 
 def _infer_comparison(context, left_values, operator, right_values):
     state = context.inference_state
+    if isinstance(operator, str):
+        operator_str = operator
+    else:
+        operator_str = str(operator.value)
     if not left_values or not right_values:
         # illegal slices e.g. cause left/right_result to be None
         result = (left_values or NO_VALUES) | (right_values or NO_VALUES)
         return _literals_to_types(state, result)
+    elif operator_str == "|" and all(
+        value.is_class() or value.is_compiled()
+        for value in itertools.chain(left_values, right_values)
+    ):
+        # ^^^ A naive hack for PEP 604
+        return ValueSet.from_sets((left_values, right_values))
     else:
         # I don't think there's a reasonable chance that a string
         # operation is still correct, once we pass something like six
diff --git a/test/completion/pep0604.py b/test/completion/pep0604.py
new file mode 100644
index 00000000..d876e8fa
--- /dev/null
+++ b/test/completion/pep0604.py
@@ -0,0 +1,46 @@
+from pep0484_generic_parameters import list_t_to_list_t
+
+list_of_ints_and_strs: list[int | str]
+
+# Test that unions are handled
+x2 = list_t_to_list_t(list_of_ints_and_strs)[0]
+#? int() str()
+x2
+
+for z in list_t_to_list_t(list_of_ints_and_strs):
+    #? int() str()
+    z
+
+
+from pep0484_generic_passthroughs import (
+    typed_variadic_tuple_generic_passthrough,
+)
+
+variadic_tuple_str_int: tuple[int | str, ...]
+
+for m in typed_variadic_tuple_generic_passthrough(variadic_tuple_str_int):
+    #? str() int()
+    m
+
+
+def func_returns_byteslike() -> bytes | bytearray:
+    pass
+
+#? bytes() bytearray()
+func_returns_byteslike()
+
+
+pep604_optional_1: int | str | None
+pep604_optional_2: None | bytes
+
+#? int() str() None
+pep604_optional_1
+
+#? None bytes()
+pep604_optional_2
+
+
+pep604_in_str: "int | bytes"
+
+#? int() bytes()
+pep604_in_str