Is rehab cheaper (or more cost effective) than jail?

It would appear that our jails are overrun with the mentally ill and drug offenses. Would it not be cost effective to put drug offenders in rehab and leave the jails for those who hurt others? It seems that we are lumping “bad behavior” into the same category. I realize that most of our jails are privatized and that there is a lot of corruption and pressure to fill them up. Well, does that actually work? Would it make more sense to try to solve the problem rather than postpone it until they get out?