diff --git a/crates/polars-core/src/utils/supertype.rs b/crates/polars-core/src/utils/supertype.rs
index 30895f9e01fe..9a73f66d8303 100644
--- a/crates/polars-core/src/utils/supertype.rs
+++ b/crates/polars-core/src/utils/supertype.rs
@@ -537,17 +537,24 @@ fn super_type_structs(fields_a: &[Field], fields_b: &[Field]) -> Option<DataType
 pub fn materialize_dyn_int(v: i128) -> AnyValue<'static> {
     // Try to get the "smallest" fitting value.
     // TODO! next breaking go to true smallest.
-    match i32::try_from(v).ok() {
-        Some(v) => AnyValue::Int32(v),
-        None => match i64::try_from(v).ok() {
-            Some(v) => AnyValue::Int64(v),
-            None => match u64::try_from(v).ok() {
-                Some(v) => AnyValue::UInt64(v),
-                None => AnyValue::Null,
-            },
-        },
+    if let Ok(v) = i32::try_from(v) {
+        return AnyValue::Int32(v);
+    }
+    if let Ok(v) = i64::try_from(v) {
+        return AnyValue::Int64(v);
+    }
+    if let Ok(v) = u64::try_from(v) {
+        return AnyValue::UInt64(v);
     }
+    #[cfg(feature = "dtype-i128")]
+    {
+        AnyValue::Int128(v)
+    }
+
+    #[cfg(not(feature = "dtype-i128"))]
+    AnyValue::Null
 }
+
 fn materialize_dyn_int_pos(v: i128) -> AnyValue<'static> {
     // Try to get the "smallest" fitting value.
     // TODO! next breaking go to true smallest.
diff --git a/py-polars/tests/unit/expr/test_literal.py b/py-polars/tests/unit/expr/test_literal.py
index 31567e7bc116..d53b52e19165 100644
--- a/py-polars/tests/unit/expr/test_literal.py
+++ b/py-polars/tests/unit/expr/test_literal.py
@@ -19,3 +19,12 @@ def test_literal_scalar_list_18686() -> None:
             ("lit2", pl.List(pl.Null)),
         ]
     )
+
+
+def test_literal_integer_20807() -> None:
+    for i in range(100):
+        value = 2**i
+        assert pl.select(pl.lit(value)).item() == value
+        assert pl.select(pl.lit(-value)).item() == -value
+        assert pl.select(pl.lit(value, dtype=pl.Int128)).item() == value
+        assert pl.select(pl.lit(-value, dtype=pl.Int128)).item() == -value
diff --git a/py-polars/tests/unit/operations/test_index_of.py b/py-polars/tests/unit/operations/test_index_of.py
index bb72e8afdfe7..7301d6dfd311 100644
--- a/py-polars/tests/unit/operations/test_index_of.py
+++ b/py-polars/tests/unit/operations/test_index_of.py
@@ -17,13 +17,21 @@
 from polars.testing import assert_frame_equal
 
 
+def isnan(value: object) -> bool:
+    if isinstance(value, int):
+        return False
+    if not isinstance(value, (np.number, float)):
+        return False
+    return np.isnan(value)  # type: ignore[no-any-return]
+
+
 def assert_index_of(
     series: pl.Series,
     value: IntoExpr,
     convert_to_literal: bool = False,
 ) -> None:
     """``Series.index_of()`` returns the index, or ``None`` if it can't be found."""
-    if isinstance(value, (np.number, float, int)) and np.isnan(value):
+    if isnan(value):
         expected_index = None
         for i, o in enumerate(series.to_list()):
             if o is not None and np.isnan(o):
@@ -93,10 +101,27 @@ def test_empty() -> None:
 
 @pytest.mark.parametrize(
     "dtype",
-    [pl.Int8, pl.Int16, pl.Int32, pl.Int64, pl.UInt8, pl.UInt16, pl.UInt32, pl.UInt64],
+    [
+        pl.Int8,
+        pl.Int16,
+        pl.Int32,
+        pl.Int64,
+        pl.UInt8,
+        pl.UInt16,
+        pl.UInt32,
+        pl.UInt64,
+        pl.Int128,
+    ],
 )
 def test_integer(dtype: pl.DataType) -> None:
-    values = [51, 3, None, 4]
+    values = [
+        51,
+        3,
+        None,
+        4,
+        pl.select(dtype.max()).item(),  # type: ignore[attr-defined]
+        pl.select(dtype.min()).item(),  # type: ignore[attr-defined]
+    ]
     series = pl.Series(values, dtype=dtype)
     sorted_series_asc = series.sort(descending=False)
     sorted_series_desc = series.sort(descending=True)
@@ -104,7 +129,7 @@ def test_integer(dtype: pl.DataType) -> None:
         [pl.Series([100, 7], dtype=dtype), series], rechunk=False
     )
 
-    extra_values = [pl.select(v).item() for v in [dtype.max(), dtype.min()]]  # type: ignore[attr-defined]
+    extra_values = [pl.select(v).item() for v in [dtype.max() - 1, dtype.min() + 1]]  # type: ignore[attr-defined]
     for s in [series, sorted_series_asc, sorted_series_desc, chunked_series]:
         value: IntoExpr
         for value in values: