FLC FAILED TO MAINTAIN ASSIGNED INTERMEDIATE DSCNT ALT WHILE ON PARADISE THREE ARR TO LAX.

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AFTER CHKING ON TO ZLA FREQ; CTLR GAVE US A NEW SQUAWK CODE AND LATER SAID WE WERE 'IN RADAR CONTACT AND CLRED TO LAX VIA THE PARADISE TWO ARR.' THIS ARR HAS SEVERAL HARD ('MUST CROSS AT') ALTS AS WELL AS SOME 'EXPECT TO CROSS' ALTS; ONE OF THEM BEING 'EXPECT TO CROSS AMIGO AT 16000 FT.' THE CTLR THEN GAVE US AMIGO AT 16000 FT. THE CAPT ASKED 'WAS IT CROSS AT OR ABOVE 16000 FT OR CROSS AT 16000 FT?' THE CTLR SAID 'DSND TO CROSS AMIGO AT 16000 FT.' WE COMPLIED WITH THIS CLRNC. AFTER XING AMIGO AT 16000 FT; THERE WAS SOME DISCUSSION BTWN THE CAPT AND I ABOUT OUR NEXT DSCNT. WE BOTH AGREED THAT OUR CLRNC WAS THE PARADISE TWO ARR WHICH INCLUDES 'CROSS TEJAY AT 12000 FT.' AT THIS POINT I BEGAN A DSCNT FOR 12000 FT. THE FREQ WAS SOMEWHAT CONGESTED AND WE DID NOT RPT LEAVING 16000 FT. SHORTLY THEREAFTER; THE CTLR ASKED US TO 'VERIFY LEVEL AT 16000 FT.' WE BOTH REALIZED THAT HE THOUGHT WE SHOULD BE AT 16000 FT. THE CAPT TURNED OFF AUTOPLT AND BEGAN TO CLB BACK TO 16000 FT FROM ABOUT 15500 FT; AND REPLIED WITH A QUESTION ABOUT THE PARADISE ARR. THE CTLR MADE OTHER XMISSIONS THEN ASKED US AGAIN TO 'VERIFY LEVEL AT 16000 FT.' THE CAPT REPLIED 'VERIFY LEVEL AT 16000 FT.' WE WERE NOW. THE CTLR RPTED TFC IN FRONT OF US XING OUR PATH. WE HAD THIS TFC IN SIGHT APPROX 2000 FT BELOW OUR ALT. SHORTLY THEREAFTER; THE CTLR CLRED US 'TO DSND VIA THE PARADISE TWO ARR.' THE REST OF THE FLT WAS UNEVENTFUL. IN CONCLUSION; IT'S VERY CONFUSING WHEN WE ARE CLRED TO DSND ON THESE TYPE ARRS; AMBIGUITY; ETC. PERHAPS SAYING 'CLRED THE PARADISE TWO ROUTING AND/OR CLRED TO DSND OR MAINTAIN FLXXX.' FREQ CONGESTION WAS ALSO A FACTOR BECAUSE THERE IS LITTLE TIME TO QUESTION/OR QUERY AN AMBIGUOUS CLRNC.