Roman aqueducts for private and public benefit

I read somewhere that wealthier families in ancient Rome were able to siphon off water from the main aqueducts leading into town, but they would take the water where it would collect in cisterns.  Pipes went forth from the cisterns at three heights; the highest piping went to the private homes, the middle pipes went to the public baths, and the lowest pipes went to public drinking water.  This was so that in times of water shortage, the more essential needs of the city would be met.  On the flip side, if you lived in a wealthy house where your water dried up on occasion, you would probably be assured of getting the cleanest water.  The dregs would naturally accumulate toward the bottom of the cisterns!