diff --git a/narwhals/_polars/namespace.py b/narwhals/_polars/namespace.py
index 45d2440b8..32e53b372 100644
--- a/narwhals/_polars/namespace.py
+++ b/narwhals/_polars/namespace.py
@@ -161,7 +161,7 @@ def concat_str(
 
         pl_exprs: list[pl.Expr] = [
             expr._native_expr  # type: ignore[attr-defined]
-            for expr in (*parse_into_exprs(*exprs, namespace=self),)
+            for expr in parse_into_exprs(*exprs, namespace=self)
         ]
 
         if self._backend_version < (0, 20, 6):
diff --git a/narwhals/dataframe.py b/narwhals/dataframe.py
index d8c68e5b6..33af048ed 100644
--- a/narwhals/dataframe.py
+++ b/narwhals/dataframe.py
@@ -74,7 +74,7 @@ def _from_compliant_dataframe(self: Self, df: Any) -> Self:
             df, level=self._level
         )
 
-    def _flatten_parse_col_names_into_expr_and_extract(
+    def _flatten_and_extract(
         self, *exprs: IntoExpr | Any, **named_exprs: IntoExpr | Any
     ) -> tuple[tuple[IntoCompliantExpr[Any]], dict[str, IntoCompliantExpr[Any]]]:
         """Process `args` and `kwargs`, extracting underlying objects as we go, interpreting strings as column names."""
@@ -91,14 +91,6 @@ def _flatten_parse_col_names_into_expr_and_extract(
         }
         return compliant_exprs, compliant_named_exprs
 
-    def _flatten_and_extract(
-        self: Self, *args: Any, **kwargs: Any
-    ) -> tuple[tuple[IntoCompliantExpr[Any]], dict[str, IntoCompliantExpr[Any]]]:
-        """Process `args` and `kwargs`, extracting underlying objects as we go."""
-        args = [self._extract_compliant(v) for v in flatten(args)]  # type: ignore[assignment]
-        kwargs = {k: self._extract_compliant(v) for k, v in kwargs.items()}
-        return args, kwargs
-
     @abstractmethod
     def _extract_compliant(self: Self, arg: Any) -> Any:
         raise NotImplementedError
@@ -138,8 +130,8 @@ def columns(self: Self) -> list[str]:
     def with_columns(
         self: Self, *exprs: IntoExpr | Iterable[IntoExpr], **named_exprs: IntoExpr
     ) -> Self:
-        compliant_exprs, compliant_named_exprs = (
-            self._flatten_parse_col_names_into_expr_and_extract(*exprs, **named_exprs)
+        compliant_exprs, compliant_named_exprs = self._flatten_and_extract(
+            *exprs, **named_exprs
         )
         return self._from_compliant_dataframe(
             self._compliant_frame.with_columns(*compliant_exprs, **compliant_named_exprs),
@@ -162,8 +154,8 @@ def select(
                 msg = f"{e!s}\n\nHint: Did you mean one of these columns: {self.columns}?"
                 raise ColumnNotFoundError(msg) from e
 
-        compliant_exprs, compliant_named_exprs = (
-            self._flatten_parse_col_names_into_expr_and_extract(*exprs, **named_exprs)
+        compliant_exprs, compliant_named_exprs = self._flatten_and_extract(
+            *exprs, **named_exprs
         )
         return self._from_compliant_dataframe(
             self._compliant_frame.select(*compliant_exprs, **compliant_named_exprs),
diff --git a/narwhals/typing.py b/narwhals/typing.py
index 041a4480a..9f9e13815 100644
--- a/narwhals/typing.py
+++ b/narwhals/typing.py
@@ -95,11 +95,6 @@ def __mod__(self, other: Any) -> Self: ...
     def __pow__(self, other: Any) -> Self: ...
 
 
-IntoCompliantExpr: TypeAlias = (
-    CompliantExpr[CompliantSeriesT_co] | str | CompliantSeriesT_co
-)
-
-
 class CompliantNamespace(Protocol, Generic[CompliantSeriesT_co]):
     def col(self, *column_names: str) -> CompliantExpr[CompliantSeriesT_co]: ...
     def lit(
@@ -287,6 +282,14 @@ class DTypes:
     Unknown: type[dtypes.Unknown]
 
 
+if TYPE_CHECKING:
+    # This one needs to be in TYPE_CHECKING to pass on 3.9,
+    # and can only be defined after CompliantExpr has been defined
+    IntoCompliantExpr: TypeAlias = (
+        CompliantExpr[CompliantSeriesT_co] | str | CompliantSeriesT_co
+    )
+
+
 __all__ = [
     "CompliantDataFrame",
     "CompliantLazyFrame",