Invalidating component drawn at multiple places

Hi,
I have a basket component and I want it to be drawn at two places in template. Since the only thing that differs is the amount of product information shown to viewer, I've decided to keep it in one component (if that's bad design, please let me know).
So I have:

{control basket}

and

{control basket:grid}

However, when I make AJAX call and try to invalidate the component in presenter via

$this->getComponent("basket")->redrawControl();

only one of visual representations is sent back as payload. Is it possible to redraw both of them this way?
Thanks for your advice.