diff --git a/src/openai/_qs.py b/src/openai/_qs.py
index de8c99bc63..ace90c5c54 100644
--- a/src/openai/_qs.py
+++ b/src/openai/_qs.py
@@ -76,9 +76,12 @@ def _stringify_item(
             items: list[tuple[str, str]] = []
             nested_format = opts.nested_format
             for subkey, subvalue in value.items():
+                if nested_format not in get_args(NestedFormat):
+                    raise NotImplementedError(
+                        f"Unknown nested_format value: {nested_format}, choose from {', '.join(get_args(NestedFormat))}"
+                    )
                 items.extend(
                     self._stringify_item(
-                        # TODO: error if unknown format
                         f"{key}.{subkey}" if nested_format == "dots" else f"{key}[{subkey}]",
                         subvalue,
                         opts,
diff --git a/src/openai/_utils/_utils.py b/src/openai/_utils/_utils.py
index 90494748cc..44d3287f46 100644
--- a/src/openai/_utils/_utils.py
+++ b/src/openai/_utils/_utils.py
@@ -276,8 +276,8 @@ def wrapper(*args: object, **kwargs: object) -> object:
                 else:
                     assert len(variants) > 0
 
-                    # TODO: this error message is not deterministic
-                    missing = list(set(variants[0]) - given_params)
+                    # preserve declaration order for deterministic error messages
+                    missing = [param for param in variants[0] if param not in given_params]
                     if len(missing) > 1:
                         msg = f"Missing required arguments: {human_join([quote(arg) for arg in missing])}"
                     else:
diff --git a/tests/test_qs.py b/tests/test_qs.py
index 697b8a95ec..bd54761dde 100644
--- a/tests/test_qs.py
+++ b/tests/test_qs.py
@@ -73,6 +73,29 @@ def test_array_brackets(method: str) -> None:
     assert unquote(serialise({"a": {"b": [True, False, None, True]}})) == "a[b][]=true&a[b][]=false&a[b][]=true"
 
 
+@pytest.mark.parametrize("method", ["class", "function"])
+def test_array_indices(method: str) -> None:
+    if method == "class":
+        serialise = Querystring(array_format="indices").stringify
+    else:
+        serialise = partial(stringify, array_format="indices")
+
+    assert unquote(serialise({"in": ["foo", "bar"]})) == "in[0]=foo&in[1]=bar"
+    assert unquote(serialise({"a": {"b": [True, False]}})) == "a[b][0]=true&a[b][1]=false"
+    assert (
+        unquote(serialise({"a": {"b": [True, False, None, True]}}))
+        == "a[b][0]=true&a[b][1]=false&a[b][3]=true"
+    )
+
+
 def test_unknown_array_format() -> None:
-    with pytest.raises(NotImplementedError, match="Unknown array_format value: foo, choose from comma, repeat"):
+    with pytest.raises(
+        NotImplementedError,
+        match="Unknown array_format value: foo, choose from comma, repeat, indices, brackets",
+    ):
         stringify({"a": ["foo", "bar"]}, array_format=cast(Any, "foo"))
+
+
+def test_unknown_nested_format() -> None:
+    with pytest.raises(NotImplementedError, match="Unknown nested_format value: foo, choose from dots, brackets"):
+        stringify({"a": {"b": "c"}}, nested_format=cast(Any, "foo"))
diff --git a/tests/test_required_args.py b/tests/test_required_args.py
index 5d1a5224ff..fec4598367 100644
--- a/tests/test_required_args.py
+++ b/tests/test_required_args.py
@@ -47,18 +47,16 @@ def foo(a: str = "", *, b: str = "", c: str = "") -> str | None:
 
     assert foo(a="a", b="b", c="c") == "a b c"
 
-    error_message = r"Missing required arguments.*"
-
-    with pytest.raises(TypeError, match=error_message):
+    with pytest.raises(TypeError, match=r"Missing required arguments: 'a', 'b' or 'c'"):
         foo()
 
-    with pytest.raises(TypeError, match=error_message):
+    with pytest.raises(TypeError, match=r"Missing required arguments: 'b' or 'c'"):
         foo(a="a")
 
-    with pytest.raises(TypeError, match=error_message):
+    with pytest.raises(TypeError, match=r"Missing required arguments: 'a' or 'c'"):
         foo(b="b")
 
-    with pytest.raises(TypeError, match=error_message):
+    with pytest.raises(TypeError, match=r"Missing required arguments: 'a' or 'b'"):
         foo(c="c")
 
     with pytest.raises(TypeError, match=r"Missing required argument: 'a'"):
@@ -78,7 +76,6 @@ def foo(*, a: str | None = None, b: str | None = None) -> str | None:
     assert foo(a=None) is None
     assert foo(b=None) is None
 
-    # TODO: this error message could probably be improved
     with pytest.raises(
         TypeError,
         match=r"Missing required arguments; Expected either \('a'\) or \('b'\) arguments to be given",