B737-700 CREW HAD ALT UNDERSHOOT WHEN GIVEN A LATE CLRNC STAR BY SCT ON THE CIVET 4 STAR INTO LAX.

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POSSIBLE ALTDEV. FLYING TO LAX; REROUTE N DUE TO WX. ZLA CLRED US DIRECT CIVET DIRECT LAX WHEN ABLE. WE WERE THEN CLRED TO FL190. I HAD THE FO CALL ZLA ABOUT OUR CLRNC AFTER CIVET. WE WERE TOLD WE WOULD FIND OUT AFTER WE SWITCHED TO SOCAL. WITH 20 MI TO CIVET THEY SWITCHED US TO SOCAL. SOCAL CLRED US DIRECT CIVET AND THE CIVET ARR. WITH JUST A FEW MI TO GO I DIALED IN THE NAVAID WHILE THE FO PROGRAMMED THE FMC. WITH 4 MI TO GO TO CIVET I ASKED THE FO TO CALL SOCAL AND TELL THEM WE WERE STILL AT FL190. THE CTLR SAID YEAH; I WAS JUST LOOKING AT THAT. HE THEN CLRED US TO CROSS ARNES AT OR ABOVE 10000 FT; CLRED TO DSND VIA THE CIVET ARR. REST OF FLT UNEVENTFUL. I CONFIRMED WITH THE FO OUR CLRNC AT CIVET AND HE SAID HE HAD HEARD CLRED CIVET AND CLRED TO DSND VIA CIVET ARR. WHEN WE RECEIVED OUR CLRNC I ACKNOWLEDGED TO THE FO CLRED DIRECT CIVET AND THE CIVET FOUR. HE DID NOT CORRECT ME NOR DIAL IN THE 14000 FT XING IN THE ALT WINDOW. SO I HAD NO IDEA WE WERE CLRED LOWER. FORTUNATELY; WE WERE THE AGGRESSOR IN REMINDING SOCAL WE WERE STILL AT FL190. WITH AN IMMEDIATE DSCNT WE WERE CLOSE TO 17000 FT AT CIVET; BUT NOT QUITE THERE. NO EXCUSES; BUT SEVERAL FACTORS. BOTH FO AND I GOT VERY LITTLE UNINTERRUPTED SLEEP AT HOTEL DUE TO FIRE ALARMS AT XA45; XB15; AND XB30. WX REROUTE AND LATE HDOF TO SOCAL THEREFORE LATE ROUTING TO LAX AND CIVET. I ONLY HEARD DIRECT CIVET AND CIVET FOUR; BUT NOT DSND VIA CIVET FOUR; POSSIBLY BECAUSE OF FOCUSED ATTN ON ROUTING. MY VERBIAGE ON ACKNOWLEDGING CLRNC TO FO COULD BE CONFUSING. FO FAILED TO NOTE I DID NOT SAY CLRED TO DSND. PNF (FO) DID NOT DIAL IN NEW ALT IN WINDOW. ATC WAS VERY BUSY AND DISTRACTED. WE HAD TO ASK/PROMPT FOR EVERY CLRNC WE GOT. SUPPLEMENTAL INFO FROM ACN 521786: PRIOR TO HDOF TO SOCAL CLRED CIVET DIRECT LAX. WE WERE AT 19000 FT. APPROX 25 NM FROM CIVET HANDED TO SOCAL; WE WERE CLRED TO DSND VIA THE CIVET ARR. CAPT ATTEMPTED TO INPUT CIVET ARR INTO FMC AND HAD SOME DIFFICULTY CLRING SOME ADDITIONAL WAYPOINTS WHICH WERE INTERFERING WITH THE ARR. HE ASKED FOR MY HELP. I THEN WORKED ON THE FMC. BY NOW WE WERE APCHING CIVET. WE BOTH REALIZED WE HAD NOT STARTED A DSCNT TO 'CROSS CIVET AT OR BELOW 17000 FT.' CAPT UNDERSTOOD CLRNC FOR THE CIVET ARR BUT DID NOT CATCH THE 'DSCNT VIA CIVET.' WE PROMPTED ATC IF WE WERE CLRED OUT OF 19000 FT. HE SAID SOMETHING TO THE EFFECT 'I THOUGHT WHEN YOU CHKED ON I CLRED YOU TO DSND VIA THE CIVET.' WE EXPEDITED OUR DSCNT; BUT CROSSED CIVET ABOVE THE 17000 FT RESTR. WE HAD NO PROB RECAPTURING THE PROFILE. RECAP: GIVEN CLRNC TO DSND VIA CIVET. I READ BACK CLRNC; BUT CAPT (PF) DID NOT COMPREHEND THE 'DSCNT VIA.' PROGRAMMING FMC AS WE NEARED CIVET. BOTH CAPT AND I REALIZED WE NEEDED TO DSND BUT CAPT THOUGHT WE NEEDED A CLRNC AND I THOUGHT HE UNDERSTOOD OUR CLRNC TO DSND. WE PROMPTED ATC. NO OTHER COMMENTS WERE MADE TO ATC AND ATC MADE NO OTHER COMMENTS TO US.