diff --git a/narwhals/_arrow/expr.py b/narwhals/_arrow/expr.py
index 1c0d0734e..df5c95367 100644
--- a/narwhals/_arrow/expr.py
+++ b/narwhals/_arrow/expr.py
@@ -283,7 +283,12 @@ def is_null(self: Self) -> Self:
     def is_nan(self: Self) -> Self:
         return reuse_series_implementation(self, "is_nan")
 
-    def is_between(self: Self, lower_bound: Any, upper_bound: Any, closed: str) -> Self:
+    def is_between(
+        self: Self,
+        lower_bound: Any,
+        upper_bound: Any,
+        closed: Literal["left", "right", "none", "both"],
+    ) -> Self:
         return reuse_series_implementation(
             self,
             "is_between",
diff --git a/narwhals/_arrow/series.py b/narwhals/_arrow/series.py
index 1e8d09827..193fc25a2 100644
--- a/narwhals/_arrow/series.py
+++ b/narwhals/_arrow/series.py
@@ -490,7 +490,10 @@ def all(self: Self, *, _return_py_scalar: bool = True) -> bool:
         )
 
     def is_between(
-        self, lower_bound: Any, upper_bound: Any, closed: str = "both"
+        self,
+        lower_bound: Any,
+        upper_bound: Any,
+        closed: Literal["left", "right", "none", "both"],
     ) -> Self:
         import pyarrow.compute as pc
 
diff --git a/narwhals/_dask/expr.py b/narwhals/_dask/expr.py
index cb20fa616..c9f8c2611 100644
--- a/narwhals/_dask/expr.py
+++ b/narwhals/_dask/expr.py
@@ -413,10 +413,9 @@ def is_between(
         self,
         lower_bound: Self | Any,
         upper_bound: Self | Any,
-        closed: str = "both",
+        closed: Literal["left", "right", "none", "both"] = "both",
     ) -> Self:
-        if closed == "none":
-            closed = "neither"
+        closed_ = "neither" if closed == "none" else closed
         return self._from_call(
             lambda _input, lower_bound, upper_bound, closed: _input.between(
                 lower_bound, upper_bound, closed
@@ -424,7 +423,7 @@ def is_between(
             "is_between",
             lower_bound=lower_bound,
             upper_bound=upper_bound,
-            closed=closed,
+            closed=closed_,
             returns_scalar=self._returns_scalar,
         )
 
diff --git a/narwhals/_pandas_like/expr.py b/narwhals/_pandas_like/expr.py
index 34d05b7eb..c694b3420 100644
--- a/narwhals/_pandas_like/expr.py
+++ b/narwhals/_pandas_like/expr.py
@@ -262,7 +262,10 @@ def clip(self, lower_bound: Any, upper_bound: Any) -> Self:
         )
 
     def is_between(
-        self, lower_bound: Any, upper_bound: Any, closed: str = "both"
+        self,
+        lower_bound: Any,
+        upper_bound: Any,
+        closed: Literal["left", "right", "none", "both"],
     ) -> Self:
         return reuse_series_implementation(
             self,
diff --git a/narwhals/_pandas_like/series.py b/narwhals/_pandas_like/series.py
index e5c5e771e..35ec672e4 100644
--- a/narwhals/_pandas_like/series.py
+++ b/narwhals/_pandas_like/series.py
@@ -263,7 +263,10 @@ def to_list(self) -> Any:
         return self._native_series.to_list()
 
     def is_between(
-        self, lower_bound: Any, upper_bound: Any, closed: str = "both"
+        self,
+        lower_bound: Any,
+        upper_bound: Any,
+        closed: Literal["left", "right", "none", "both"],
     ) -> PandasLikeSeries:
         ser = self._native_series
         _, lower_bound = broadcast_align_and_extract_native(self, lower_bound)
diff --git a/narwhals/_spark_like/expr.py b/narwhals/_spark_like/expr.py
index 66826a6ab..03529ca96 100644
--- a/narwhals/_spark_like/expr.py
+++ b/narwhals/_spark_like/expr.py
@@ -3,6 +3,7 @@
 from typing import TYPE_CHECKING
 from typing import Any
 from typing import Callable
+from typing import Literal
 from typing import Sequence
 
 from narwhals._expression_parsing import infer_new_root_output_names
@@ -276,7 +277,7 @@ def is_between(
         self,
         lower_bound: Any,
         upper_bound: Any,
-        closed: str,
+        closed: Literal["left", "right", "none", "both"],
     ) -> Self:
         def _is_between(_input: Column, lower_bound: Any, upper_bound: Any) -> Column:
             if closed == "both":
diff --git a/narwhals/expr.py b/narwhals/expr.py
index 653300da8..807a7f04b 100644
--- a/narwhals/expr.py
+++ b/narwhals/expr.py
@@ -1792,10 +1792,10 @@ def sort(self, *, descending: bool = False, nulls_last: bool = False) -> Self:
 
     # --- transform ---
     def is_between(
-        self,
+        self: Self,
         lower_bound: Any | IntoExpr,
         upper_bound: Any | IntoExpr,
-        closed: str = "both",
+        closed: Literal["left", "right", "none", "both"] = "both",
     ) -> Self:
         """Check if this expression is between the given lower and upper bounds.
 
diff --git a/narwhals/series.py b/narwhals/series.py
index 7b4cfbf6e..8385b43ad 100644
--- a/narwhals/series.py
+++ b/narwhals/series.py
@@ -2605,7 +2605,10 @@ def fill_null(
         )
 
     def is_between(
-        self, lower_bound: Any | Self, upper_bound: Any | Self, closed: str = "both"
+        self: Self,
+        lower_bound: Any | Self,
+        upper_bound: Any | Self,
+        closed: Literal["left", "right", "none", "both"] = "both",
     ) -> Self:
         """Get a boolean mask of the values that are between the given lower/upper bounds.