A B737 CAPT RPTED THAT HIS FLT ATTENDANT CREW WAS NOT WELL RESTED UPON RPTING FOR DUTY AT MIA.

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I WAS CAPT OF FLT. UPON ARR AT ACFT; I WAS INFORMED BY FLT ATTENDANT CREW THAT THEY WERE VERY TIRED AND HAD VERY LITTLE SLEEP ON LAYOVER. I PULLED UP COMPUTER INFO TO VERIFY THEIR STORY. THEY ALL LOOKED VERY TIRED. UPON REVIEW OF THEIR SEQUENCE; I DETERMINED THEY HAD 6 HRS 15 MINS BEHIND THE DOOR. ALLOWING FOR 1 HR GET UP TIME AND MINIMUM OF 15 MINS TO UNDRESS; PREPARE; AND GO TO SLEEP; THEY HAD APPROX 5 HRS 30 MINS SLEEP. THIS IS INADEQUATE AND UNSAFE. FURTHER REVIEW INDICATED THAT THEIR NEXT LAYOVER AFTER LIMO TRIP FROM XXX WOULD BE SIMILAR AND NOT ALLOW SUFFICIENT SLEEP TIME. I PULLED UP THE SEQUENCE THIS AM AND DETERMINED THAT; ALTHOUGH THEY WERE REQUIRED A 10 HR LAYOVER; THEY GOT 9 HRS BEHIND THE DOOR AND APPROX 7 HRS AND 30 MINS TO SLEEP AFTER MINIMUM SLEEP THE PREVIOUS NIGHT. THE DEP TIME WAS SLIPPED 1 HR TO GIVE THEM THE MINIMUM RESULTING IN EXCESSIVE INCONVENIENCE TO OUR PAX AND OUR RELIABILITY. I OFFERED TO REMOVE THE CREW AT MIA FOR FATIGUE BUT THEY BEGGED TO FLY BECAUSE OF THE LOSS OF PAY AND COMPANY HARASSMENT ASSOCIATED WITH FLT ATTENDANT SICK CALLS. IN HINDSIGHT; I SHOULD HAVE REMOVED THE CREW AND WILL DO SO NEXT TIME. THIS ACT OF MINIMUM FLT ATTENDANT CREWS ASSOCIATED WITH UNREALISTIC SLEEP ON LAYOVERS CAN ONLY NEGATIVELY AFFECT THE SAFETY OF OUR OP AND SHOULD BE CHANGED IMMEDIATELY.