diff --git a/manimlib/camera/camera_frame.py b/manimlib/camera/camera_frame.py
index c126053c..648d55cd 100644
--- a/manimlib/camera/camera_frame.py
+++ b/manimlib/camera/camera_frame.py
@@ -29,9 +29,11 @@ class CameraFrame(Mobject):
         # Field of view in the y direction
         fovy: float = 45 * DEGREES,
         euler_axes: str = "zxz",
+        # This keeps it ordered first in a scene
+        z_index=-1,
         **kwargs,
     ):
-        super().__init__(**kwargs)
+        super().__init__(z_index=z_index, **kwargs)
 
         self.uniforms["orientation"] = Rotation.identity().as_quat()
         self.uniforms["fovy"] = fovy
diff --git a/manimlib/mobject/mobject.py b/manimlib/mobject/mobject.py
index 2dfbb812..a09d6116 100644
--- a/manimlib/mobject/mobject.py
+++ b/manimlib/mobject/mobject.py
@@ -94,7 +94,6 @@ class Mobject(object):
         self.texture_paths = texture_paths
         self.depth_test = depth_test
         self.z_index = z_index
-        self._scene_order = 0
 
         # Internal state
         self.submobjects: list[Mobject] = []
@@ -1246,6 +1245,10 @@ class Mobject(object):
     def set_z(self, z: float, direction: Vect3 = ORIGIN) -> Self:
         return self.set_coord(z, 2, direction)
 
+    def set_z_index(self, z_index: int) -> Self:
+        self.z_index = z_index
+        return self
+
     def space_out_submobjects(self, factor: float = 1.5, **kwargs) -> Self:
         self.scale(factor, **kwargs)
         for submob in self.submobjects:
diff --git a/manimlib/scene/scene.py b/manimlib/scene/scene.py
index 5fab8f85..f73fb088 100644
--- a/manimlib/scene/scene.py
+++ b/manimlib/scene/scene.py
@@ -414,13 +414,12 @@ class Scene(object):
         foreground in the order with which they are added.
         """
         self.remove(*new_mobjects)
-        idx = 0
-        scene_order = len(self.mobjects)
-        for m in new_mobjects:
-            m._scene_order = scene_order+idx
-            idx += 1
         self.mobjects += new_mobjects
-        self.mobjects = [self.mobjects[0]]+sorted(self.mobjects[1:], key=lambda m:(m.z_index, m._scene_order))
+
+        # Reorder based on z_index
+        id_to_scene_order = {id(m): idx for idx, m in enumerate(self.mobjects)}
+        self.mobjects.sort(key=lambda m: (m.z_index, id_to_scene_order[id(m)]))
+
         self.id_to_mobject_map.update({
             id(sm): sm
             for m in new_mobjects