Attaching drywall to cracked/sagging plaster ceiling?

I have a plaster & lath ceiling in a bedroom that is in need of repair – it's intact for the most part, but it's pretty unsightly. Since the entire ceiling is full of cracks, I'd rather simply cover it with a layer of 1/2" sheet rock.

Would the drywall be sufficient to clamp the sagging parts to the lath/studs, or should I use plaster washers and then attach the drywall? I know furring strips and then drywall would probably be the safest bet, but I'd rather try to keep as much ceiling height as possible.

Thanks