B737 CREW WOULD NOT HAVE COMPLIED WITH A XING RESTR. INFORMED ATC AND GOT RESTR WAIVED.

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WE WERE CLRED TO CROSS 25 NM N OF VULCAN (VUH) VOR ON DSCNT INTO BIRMINGHAM. FO INADVERTENTLY PUT 11000 FT AT VULCAN VOR AFTER ENTERING A POS FOR 25 MI N. I WAS GETTING ATIS FOR BHM AT THE TIME. THE ATIS THEN CHANGED; AND I WAS BUSY GETTING THE NEW ATIS JUST PRIOR TO DSCNT. I DID NOT NOTICE 11000 FT AT VUZ ON CDU. AS WE BEGAN DSCNT; WE NOTICED WE WOULD BE HIGH. WE TOLD BHM APCH THAT WE WERE HIGH AND NEEDED THE XING RESTR WAIVED; OR A VECTOR OFF COURSE. HE WAS WORKING AT LEAST 2 DIFFERENT FREQS; BUT DID RELIEVE THE XING RESTR AND GAVE US A TURN OFF COURSE; EVEN THOUGH RADIO WAS CONGESTED. WE APOLOGIZED TO CTLR; AND I CALLED BHM APCH ON THE PHONE FROM BHM OPS TO APOLOGIZE. THE CTLR ON THE PHONE SAID IT WAS NOT A PROB AND ALL WAS OK. I SHOULD HAVE CHKED THE CDU AND SHOULD HAVE BEEN MORE OBSERVANT ON MILEAGE DME BEFORE UPDATING ATIS. WE WERE DEFINITELY RELIEVED OF THIS XING RESTR BEFORE WE GOT TO 25 DME POINT; AND CTLR TURNED US PRIOR TO 25 DME. WE JUST WANTED TO SUBMIT THIS TO BE ON THE SAFE SIDE.