diff --git a/bigframes/core/array_value.py b/bigframes/core/array_value.py
index b20c6561ea..5a573694ae 100644
--- a/bigframes/core/array_value.py
+++ b/bigframes/core/array_value.py
@@ -212,11 +212,17 @@ def filter(self, predicate: ex.Expression):
             return arr.drop_columns(filter_ids)
 
     def order_by(
-        self, by: Sequence[OrderingExpression], is_total_order: bool = False
+        self,
+        by: Sequence[OrderingExpression],
+        is_total_order: bool = False,
+        stable: bool = True,
     ) -> ArrayValue:
         return ArrayValue(
             nodes.OrderByNode(
-                child=self.node, by=tuple(by), is_total_order=is_total_order
+                child=self.node,
+                by=tuple(by),
+                is_total_order=is_total_order,
+                stable=stable,
             )
         )
 
diff --git a/bigframes/core/blocks.py b/bigframes/core/blocks.py
index 239eedf6d3..c86e4e2baf 100644
--- a/bigframes/core/blocks.py
+++ b/bigframes/core/blocks.py
@@ -395,9 +395,10 @@ def cols_matching_label(self, partial_label: Label) -> typing.Sequence[str]:
     def order_by(
         self,
         by: typing.Sequence[ordering.OrderingExpression],
+        stable: bool = True,
     ) -> Block:
         return Block(
-            self._expr.order_by(by),
+            self._expr.order_by(by, stable=stable),
             index_columns=self.index_columns,
             column_labels=self.column_labels,
             index_labels=self.index.names,
diff --git a/bigframes/core/indexes/base.py b/bigframes/core/indexes/base.py
index f7438307f7..894f3bbb89 100644
--- a/bigframes/core/indexes/base.py
+++ b/bigframes/core/indexes/base.py
@@ -436,6 +436,7 @@ def sort_values(
         *,
         inplace: bool = False,
         ascending: bool = True,
+        kind: __builtins__.str | None = None,
         na_position: __builtins__.str = "last",
     ) -> Index:
         if na_position not in ["first", "last"]:
@@ -448,7 +449,8 @@ def sort_values(
             else order.descending_over(column, na_last)
             for column in index_columns
         ]
-        return Index(self._block.order_by(ordering))
+        is_stable = (kind or constants.DEFAULT_SORT_KIND) in ["stable", "mergesort"]
+        return Index(self._block.order_by(ordering, stable=is_stable))
 
     def astype(
         self,
diff --git a/bigframes/core/nodes.py b/bigframes/core/nodes.py
index 6071eaeaea..470c766c74 100644
--- a/bigframes/core/nodes.py
+++ b/bigframes/core/nodes.py
@@ -992,7 +992,8 @@ def remap_refs(
 @dataclasses.dataclass(frozen=True, eq=False)
 class OrderByNode(UnaryNode):
     by: Tuple[OrderingExpression, ...]
-    # This is an optimization, if true, can discard previous orderings.
+    stable: bool = True
+    # This is an optimization, if true, can discard previous orderings, even if doing a stable sort
     # might be a total ordering even if false
     is_total_order: bool = False
 
diff --git a/bigframes/core/rewrite/order.py b/bigframes/core/rewrite/order.py
index 6741dfddad..382af92d66 100644
--- a/bigframes/core/rewrite/order.py
+++ b/bigframes/core/rewrite/order.py
@@ -71,7 +71,8 @@ def pull_up_order_inner(
             child_result, child_order = pull_up_order_inner(node.child)
             return child_result, child_order.with_reverse()
         elif isinstance(node, bigframes.core.nodes.OrderByNode):
-            if node.is_total_order:
+            # unstable sorts don't care about previous order, total orders override previous order
+            if (not node.stable) or node.is_total_order:
                 new_node = remove_order(node.child)
             else:
                 new_node, child_order = pull_up_order_inner(node.child)
@@ -106,6 +107,10 @@ def pull_up_order_inner(
                         ),
                     )
                 )
+            elif not node.stable:
+                new_order = bigframes.core.ordering.RowOrdering(
+                    ordering_value_columns=tuple(new_by),
+                )
             else:
                 assert child_order
                 new_order = child_order.with_ordering_columns(new_by)
diff --git a/bigframes/dataframe.py b/bigframes/dataframe.py
index 25cedda8f4..79412c0732 100644
--- a/bigframes/dataframe.py
+++ b/bigframes/dataframe.py
@@ -2390,6 +2390,7 @@ def sort_index(
         *,
         ascending: bool = ...,
         inplace: Literal[False] = ...,
+        kind: str = ...,
         na_position: Literal["first", "last"] = ...,
     ) -> DataFrame:
         ...
@@ -2400,6 +2401,7 @@ def sort_index(
         *,
         ascending: bool = ...,
         inplace: Literal[True] = ...,
+        kind: str = ...,
         na_position: Literal["first", "last"] = ...,
     ) -> None:
         ...
@@ -2410,6 +2412,7 @@ def sort_index(
         axis: Union[int, str] = 0,
         ascending: bool = True,
         inplace: bool = False,
+        kind: str | None = None,
         na_position: Literal["first", "last"] = "last",
     ) -> Optional[DataFrame]:
         if utils.get_axis_number(axis) == 0:
@@ -2423,7 +2426,8 @@ def sort_index(
                 else order.descending_over(column, na_last)
                 for column in index_columns
             ]
-            block = self._block.order_by(ordering)
+            is_stable = (kind or constants.DEFAULT_SORT_KIND) in ["stable", "mergesort"]
+            block = self._block.order_by(ordering, stable=is_stable)
         else:  # axis=1
             _, indexer = self.columns.sort_values(
                 return_indexer=True, ascending=ascending, na_position=na_position  # type: ignore
@@ -2467,7 +2471,7 @@ def sort_values(
         *,
         inplace: bool = False,
         ascending: bool | typing.Sequence[bool] = True,
-        kind: str = "quicksort",
+        kind: str | None = None,
         na_position: typing.Literal["first", "last"] = "last",
     ) -> Optional[DataFrame]:
         if isinstance(by, (bigframes.series.Series, indexes.Index, DataFrame)):
@@ -2499,7 +2503,8 @@ def sort_values(
                 if is_ascending
                 else order.descending_over(column_id, na_last)
             )
-        block = self._block.order_by(ordering)
+        is_stable = (kind or constants.DEFAULT_SORT_KIND) in ["stable", "mergesort"]
+        block = self._block.order_by(ordering, stable=is_stable)
         if inplace:
             self._set_block(block)
             return None
diff --git a/bigframes/series.py b/bigframes/series.py
index 23799a0a43..4c37ba5ae5 100644
--- a/bigframes/series.py
+++ b/bigframes/series.py
@@ -1801,19 +1801,21 @@ def sort_values(
         axis=0,
         inplace: bool = False,
         ascending=True,
-        kind: str = "quicksort",
+        kind: str | None = None,
         na_position: typing.Literal["first", "last"] = "last",
     ) -> Optional[Series]:
         if axis != 0 and axis != "index":
             raise ValueError(f"No axis named {axis} for object type Series")
         if na_position not in ["first", "last"]:
             raise ValueError("Param na_position must be one of 'first' or 'last'")
+        is_stable = (kind or constants.DEFAULT_SORT_KIND) in ["stable", "mergesort"]
         block = self._block.order_by(
             [
                 order.ascending_over(self._value_column, (na_position == "last"))
                 if ascending
                 else order.descending_over(self._value_column, (na_position == "last"))
             ],
+            stable=is_stable,
         )
         if inplace:
             self._set_block(block)
@@ -1823,19 +1825,37 @@ def sort_values(
 
     @typing.overload  # type: ignore[override]
     def sort_index(
-        self, *, axis=..., inplace: Literal[False] = ..., ascending=..., na_position=...
+        self,
+        *,
+        axis=...,
+        inplace: Literal[False] = ...,
+        ascending=...,
+        kind: str = ...,
+        na_position=...,
     ) -> Series:
         ...
 
     @typing.overload
     def sort_index(
-        self, *, axis=0, inplace: Literal[True] = ..., ascending=..., na_position=...
+        self,
+        *,
+        axis=0,
+        inplace: Literal[True] = ...,
+        ascending=...,
+        kind: str = ...,
+        na_position=...,
     ) -> None:
         ...
 
     @validations.requires_index
     def sort_index(
-        self, *, axis=0, inplace: bool = False, ascending=True, na_position="last"
+        self,
+        *,
+        axis=0,
+        inplace: bool = False,
+        ascending=True,
+        kind: str | None = None,
+        na_position="last",
     ) -> Optional[Series]:
         # TODO(tbergeron): Support level parameter once multi-index introduced.
         if axis != 0 and axis != "index":
@@ -1850,7 +1870,8 @@ def sort_index(
             else order.descending_over(column, na_last)
             for column in block.index_columns
         ]
-        block = block.order_by(ordering)
+        is_stable = (kind or constants.DEFAULT_SORT_KIND) in ["stable", "mergesort"]
+        block = block.order_by(ordering, stable=is_stable)
         if inplace:
             self._set_block(block)
             return None
diff --git a/third_party/bigframes_vendored/constants.py b/third_party/bigframes_vendored/constants.py
index 9705b19c90..fc698ea188 100644
--- a/third_party/bigframes_vendored/constants.py
+++ b/third_party/bigframes_vendored/constants.py
@@ -55,3 +55,5 @@
     "_deferred",
 ]
 VALID_WRITE_ENGINES = typing.get_args(WriteEngineType)
+
+DEFAULT_SORT_KIND = "stable"
diff --git a/third_party/bigframes_vendored/pandas/core/frame.py b/third_party/bigframes_vendored/pandas/core/frame.py
index f04d9989dd..2d62add6a8 100644
--- a/third_party/bigframes_vendored/pandas/core/frame.py
+++ b/third_party/bigframes_vendored/pandas/core/frame.py
@@ -2210,7 +2210,7 @@ def sort_values(
         *,
         inplace: bool = False,
         ascending: bool | Sequence[bool] = True,
-        kind: str = "quicksort",
+        kind: str | None = None,
         na_position: Literal["first", "last"] = "last",
     ):
         """Sort by the values along row axis.
@@ -2296,7 +2296,7 @@ def sort_values(
                 the by.
             inplace (bool, default False):
                 If True, perform operation in-place.
-            kind (str, default 'quicksort'):
+            kind (str, default None):
                 Choice of sorting algorithm. Accepts 'quicksort', 'mergesort',
                 'heapsort', 'stable'. Ignored except when determining whether to
                 sort stably. 'mergesort' or 'stable' will result in stable reorder.
@@ -2320,6 +2320,7 @@ def sort_index(
         axis: str | int = 0,
         ascending: bool = True,
         inplace: bool = False,
+        kind: str | None = None,
         na_position: Literal["first", "last"] = "last",
     ):
         """Sort object by labels (along an axis).
@@ -2332,6 +2333,10 @@ def sort_index(
                 Sort ascending vs. descending.
             inplace (bool, default False):
                 Whether to modify the DataFrame rather than creating a new one.
+            kind (str, default None):
+                Choice of sorting algorithm. Accepts 'quicksort', 'mergesort',
+                'heapsort', 'stable'. Ignored except when determining whether to
+                sort stably. 'mergesort' or 'stable' will result in stable reorder.
             na_position ({'first', 'last'}, default 'last'):
                 Puts NaNs at the beginning if `first`; `last` puts NaNs at the end.
                 Not implemented for MultiIndex.
diff --git a/third_party/bigframes_vendored/pandas/core/indexes/base.py b/third_party/bigframes_vendored/pandas/core/indexes/base.py
index d21056a8cf..9933903b10 100644
--- a/third_party/bigframes_vendored/pandas/core/indexes/base.py
+++ b/third_party/bigframes_vendored/pandas/core/indexes/base.py
@@ -828,7 +828,11 @@ def nunique(self) -> int:
         raise NotImplementedError(constants.ABSTRACT_METHOD_ERROR_MESSAGE)
 
     def sort_values(
-        self, *, ascending: bool = True, na_position: str = "last"
+        self,
+        *,
+        ascending: bool = True,
+        kind: str | None = None,
+        na_position: str = "last",
     ) -> Index:
         """
         Return a sorted copy of the index.
@@ -851,6 +855,10 @@ def sort_values(
         Args:
             ascending (bool, default True):
                 Should the index values be sorted in an ascending order.
+            kind (str, default None):
+                Choice of sorting algorithm. Accepts 'quicksort', 'mergesort',
+                'heapsort', 'stable'. Ignored except when determining whether to
+                sort stably. 'mergesort' or 'stable' will result in stable reorder.
             na_position ({'first' or 'last'}, default 'last'):
                 Argument 'first' puts NaNs at the beginning, 'last' puts NaNs at
                 the end.
diff --git a/third_party/bigframes_vendored/pandas/core/series.py b/third_party/bigframes_vendored/pandas/core/series.py
index 775971ab35..fee1a42a37 100644
--- a/third_party/bigframes_vendored/pandas/core/series.py
+++ b/third_party/bigframes_vendored/pandas/core/series.py
@@ -1458,7 +1458,7 @@ def sort_values(
         axis: Axis = 0,
         inplace: bool = False,
         ascending: bool | int | Sequence[bool] | Sequence[int] = True,
-        kind: str = "quicksort",
+        kind: str | None = None,
         na_position: str = "last",
     ):
         """
@@ -1535,7 +1535,7 @@ def sort_values(
                 Whether to modify the Series rather than creating a new one.
             ascending (bool or list of bools, default True):
                 If True, sort values in ascending order, otherwise descending.
-            kind (str, default to 'quicksort'):
+            kind (str, default to None):
                 Choice of sorting algorithm. Accepts quicksort', 'mergesort',
                 'heapsort', 'stable'. Ignored except when determining whether to
                 sort stably. 'mergesort' or 'stable' will result in stable reorder
@@ -1555,6 +1555,7 @@ def sort_index(
         axis: Axis = 0,
         inplace: bool = False,
         ascending: bool | Sequence[bool] = True,
+        kind: str | None = None,
         na_position: NaPosition = "last",
     ):
         """
@@ -1602,6 +1603,10 @@ def sort_index(
             ascending (bool or list-like of bools, default True):
                 Sort ascending vs. descending. When the index is a MultiIndex the
                 sort direction can be controlled for each level individually.
+            kind (str, default None):
+                Choice of sorting algorithm. Accepts 'quicksort', 'mergesort',
+                'heapsort', 'stable'. Ignored except when determining whether to
+                sort stably. 'mergesort' or 'stable' will result in stable reorder.
             na_position ({'first', 'last'}, default 'last'):
                 If 'first' puts NaNs at the beginning, 'last' puts NaNs at the end.
                 Not implemented for MultiIndex.