You can occasionally find a company that will rent to under-21's -- but they are few and the costs will be high -- they will no doubt charge you a premium for their "extra risk."

These are typically going to be smaller, more local companies rather than the national "majors." A quick look through the Phoenix business telephone directory showed one agency (Saban's) that specifically said they will rent to under-21's -- and two others that MAY (their ads simply said under-25 OK, so I do not know what the cut-off age is, if any).