AN AIR CARRIER PILOT COMMENTS THAT ATC ALTITUDE CONSTRAINT CLEARANCES WITH MORE THAN ONE CONSTRAINED FIX IN A SINGLE CLEARANCE CAN CAUSE CREWS TO MISS DOWN TRACK ALTITUDE CONSTRAINTS BECAUSE OF WORK DISTRACTIONS.

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ENRTE TO TPA ON THE DADES1 ARR; WE WERE GIVEN A DSCNT TO CROSS JAYJA AT FL270. AT SOME POINT; EITHER JUST BEFORE OR AFTER WE STARTED OUR DSCNT; WE WERE GIVEN ANOTHER CLRNC TO 'DSND TO FL260; PREVIOUS RESTR APPLIES.' I WAS PM AND LEFT 270 IN THE ALT WINDOW TO MAKE SURE WE LEVELED AT JAYJA. I MADE A NOTE ON MY RELEASE TO CONTINUE DSCNT TO 260 AFTER JAYJA. AT THE TIME; THE FO AND I DISCUSSED HOW MUCH WE HATED GETTING CLRNCS LIKE WE'D JUST RECEIVED BECAUSE OF THE POSSIBILITY OF DISTR OR THAT WE MIGHT JUST FORGET TO CONTINUE THE DSCNT AFTER LEVELING OFF. SURE ENOUGH; DURING OUR DSCNT TO FL270; WE GOT AN OFF SCHEDULE DSCNT LIGHT; FOLLOWED SHORTLY BY A CABIN ALT AUTO FAIL LIGHT. AS WE RAN THE QRH PROCS; THE FO LEVELED AT FL270 SHORT OF JAYJA AND RESET THE PWR. FINISHING THE QRH PROCS; I TURNED ON THE SEATBELT SIGN AND MADE AN ANNOUNCEMENT TO THE BACK; AS IT WAS STARTING TO GET A LITTLE BUMPY. WHILE I WAS OFF FREQ; THE FO TOOK A CALL FROM ZJX INFORMING US WE WERE 10 MI S OF JAYJA AND HAD BEEN INSTRUCTED TO DSND TO FL260 AFTER JAYJA. WE BEGAN THE DSCNT AT THAT TIME AND NOTHING FURTHER WAS SAID. WE GOT BIT BY EXACTLY WHAT WE HAD DISCUSSED AFTER RECEIVING THE CLRNC. WE MISSED THE DSCNT AND IT WAS OUR FAULT. HOWEVER; I STRONGLY DISAGREE WITH ATC'S SEEMINGLY INCREASED USE OF CLRNCS LIKE WE RECEIVED. I WOULD LIKE TO SEE ATC REFRAIN FROM GIVING MULTIPLE ALT CLRNCS LIKE WE RECEIVED. IT'S ONE THING TO DSND VIA AN ARR WITH PUBLISHED ALT RESTRS WHERE WE CAN REF AN APCH CHART AND THE LEGS PAGE ON THE COMPUTER; BUT TO GET RANDOM CLRNCS LIKE WE GOT IS SOMETHING ELSE. AFTER RECEIVING OUR CLRNC; WE EVEN DISCUSSED HOW EASY IT WOULD BE TO MISS THE DSCNT AFTER LEVELING OFF AND WE STILL SCREWED IT UP!