ACR PLT REQUESTS BETTER PLANNING AND TIMELY APCH ROUTING ASSIGNMENT FOR LAX ARR FROM ATC.

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I WOULD LIKE TO ENLIST YOUR HELP IN ENCOURAGING ATC TO PROVIDE EARLY SPECIFIC ARRIVAL INSTRUCTIONS; PARTICULARLY ON POTENTIAL; MULTIPLE STAR TRANSITION POSSIBILITIES; SO AS TO ENHANCE FLT SAFETY DURING EXTRMELY DEMANDING STAR'S INTO KLAX. IN THIS CASE WE HAD STUDIED ALL POTENTIAL STAR'S INTO LAX. WE WERE ORIGINALLY FILED VIA THE 'PDZ-3' ARRIVAL OUR ROUTING HAD CHANGED SOMEWHAT; DUE TO THUNDERSTORMS OVER NM; AZ; AND CO. SO; WE WERE PROCEEDING OVER HEC VOR. WE HAD LOADED THE NEW 'YENNI' STAR INTO RTE #1 OF THE FMC; ANTICIPATING AN ILS 25L APCH. WE ALSO LOADED THE 'MITTS' STAR; INTO THE RTE #2 DATABASE; JUST IN CASE WE WERE RE-ROUTED FOR AN ILS 24R APCH. AFTER 4 HRS OF PREPARATION AND REVIEW; WE THOUGHT THAT WE WERE ADAPTABLE TO MOST ANY POSSIBILITY! THE ACFT WAS ON AUTOPLT; SO THAT WE COULD FLY THE ARRIVAL AS SAFELY AND ACCURATELY AS POSSIBLE. AS WE FLEW PAST HEC VOR; WE STILL WERE UNABLE TO GET A COMMITMENT FROM ATC ON WHICH STAR WE WOULD BE ISSUED FOR OUR ARRIVAL INTO LAX. NOW AT AN INTERMIEDIATE ALTITUDE OF 24000 MSL; WE WERE ISSUED THE CIVET ARRIVAL. ALTHOUGH WE ADAPTED QUICKLY TO AN ARRIVAL THAT WE LEAST EXPECTED; BECAUSE THE ARRIVAL PROC (CIVET STAR) WAS ISSUED RELATIVELY 'LATE'; AND AT THE LAST MIN; WE WERE IMMEDIATELY 'HIGH' ON THE XING RESTRICTION OVER CIVET. SO; I DISCONNECTED THE AUTOPLT; AND ACCELERATED OUR DESCENT; AND COMPLIED WITH THE ALTITUDE RESTRICTIONS FOR CIVET; ABOUT (4) FOUR MI W OF CIVET. WE HAD CROSSED CIVET BTWN FL175 AND FL180; ABOUT 500-1000 FT HIGH. WE HAD BEEN UNABLE TO ADVISE ATC DUE TO FREQ CONGESTION. OUR ARR WAS SIMILAR TO A SOCCER GOALLY WAITING FOR MULTIPLE PLAYERS TO KICK A SOCCER BALL AT HIS NET; FROM VARIOUS POS ON THE FIELD; NOT KNOWING FROM WHICH PART OF THE FIELD; THE BALL WOULD ACTUALLY BE KICKED FROM;UNTIL IT WAS ACTUALLY KICKED! THESE STAR'S ARE COMPLEX ENOUGH THAT THEY NEED TO BE ISSUED; WELL IN ADVANCE OF THE ARR PORTION OF THE FLT; PARTICULLARLY; WHEN THERE ARE MULTIPLE STAR'S AND TRANSITION POSSIBILITIES INTO A COMPLEX ARR ENVIROMENT; WITH MULTIPLE APCHS AND RWYS!!!