LESS THAN STANDARD SEPARATION BETWEEN 2 ACR. OPERATIONAL ERROR.

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OUR FLT; ACR X; WAS DSNDING FROM ALT WHILE FLYING A DIRECT COURSE TO THE BOULDER CITY VOR FOR LNDG IN LAS. THE F/O WAS FLYING AND I WAS ON THE RADIO ZLA GAVE US A 10 DEG COURSE CHANGE TO THE LEFT FOR TFC AS WE WERE PASSING APPROX 26000'. A FEW MINS LATER WE WERE GIVEN ANOTHER 15 DEG LEFT VECTOR FOR COMPANY TFC THAT WAS CLBING OUT OF LAS. THE CTLR CALLED THE POS OF OUR TFC AND I COULD SEE THE OTHER MLG. IT APPEARED TO BE ABOUT 3 MI AWAY; AND LOOKED LIKE IT WOULD PASS WELL TO OUR RIGHT. AT ABOUT THAT TIME; AS WE WERE PASSING 21500'; THE CTLR SUDDENLY TOLD US TO LEVEL AT FL220 AND OUR COMPANY FLT TO STOP HIS CLB AT FL210. WE STOPPED OUR DSCNT AT ABOUT FL210 AS OUR COMPANY PASSED ABEAM 2-3 MI AWAY. WHEN WE WERE TOLD TO STOP AT FL220 I TOLD THE CTLR WE WERE ALREADY AT 21500'. AFTER WE PASSED I ASKED THE CTLR IF HE WANTED US TO CONTINUE OUR DSCNT AND HE SAID YES. I SAW THE OTHER ACFT FOR SOME TIME BEFORE AND AS WE PASSED; AND NEVER FELT THERE WAS ANY CONFLICT. THE CTLR SOUNDED PRETTY TENSE ABOUT IT WHEN HE GAVE US OUR LATE LEVEL OFF CALL. I'M NOT SURE WHAT THE PROB WAS. EVIDENTLY THE CTLR DIDN'T SEE UNTIL TOO LATE THAT ON OUR VECTORS; WE WOULD NOT KEEP MINIMUM SEP ALTHOUGH IT LOOKED TO ME AS THOUGH WE HAD MORE THAN ENOUGH SEP THE WHOLE TIME.