ZAB CONTROLLER EXPERIENCED OPERATIONAL ERROR AT 10000 FT WHEN DESCENDING AIRCRAFT THROUGH OCCUPIED ALTITUDE; FAILING TO SEE CONFLICTING TRAFFIC BECAUSE OF VFR DATA BLOCK COVERING INFORMATION.

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I HAD JUST SAT DOWN TO WORK THE ARR PUSH INTO PHOENIX FROM THE W COAST; AND HAD SEVERAL ITEMS TO DO AS WELL AS SEVERAL CLRNCS TO ISSUE. THERE WERE ABOUT 10 IFR ACFT AND 4 VFR ACFT ON FREQ. I HAD A MIL ACFT X THAT WAS REQUESTING A DEST CHANGE IN PHOENIX'S AIRSPACE; AND SEVERAL IFR JETS INBOUND TO PHOENIX. THERE WAS AN ASSISTANT CTLR TRAINEE THAT WAS RECEIVING OJT ON THE D-SIDE OF THE SECTOR I WAS WORKING. WHEN THE ERROR OCCURRED; HE AND HIS INSTRUCTOR WERE ONLINE; BUT WERE TALKING ABOUT THE MIL CHANGE IN DEST. THE 2 ACFT THAT BECAME IN CONFLICT WERE X AND Y. ACFT Y WAS TRAVELING WBOUND AT 10000 FT. ACFT X WAS INBOUND TO PHOENIX AT 11000 FT. I ISSUED ACFT X A 100 DEG HDG TO JOIN THE BLH4 ARR. PER THE ARR; ACFT X NEEDS TO BE AT 10000 FT MSL BY PHOENIX BOUNDARY. I ISSUED ACFT X A DSCNT TO 10000 FT BECAUSE I HAD A LOT OF OTHER THINGS GOING ON AND I WANTED TO GET HIM OUT OF THE WAY OF THE JET TFC INBOUND TO PHOENIX. (THE JETS DSND TO 11000 FT.) AT THE TIME; I HAD SEVERAL DATA BLOCKS IN THE VICINITY OF ABC INTXN. ALTHOUGH THERE WAS NO DATA BLOCK OVERLAP; A VFR DATA BLOCK WAS COVERING THE TAG OF ACFT Y. AFTER ISSUING THE DSCNT CLRNC TO ACFT X; I GAVE A CLRNC TO ACFT Y FOR HIS CHANGE IN DEST. HE READ BACK PART OF THE CLRNC AND THEN STATED I WAS BROKEN AND COULD I REPEAT AFTER BLH VOR. WHILE I REISSUED ACFT Y HIS CLRNC; ACFT X WAS DSNDING TO 10000 FT. I DID NOT HAVE A J-RING (OR HALO) ON EITHER ACFT X OR ACFT Y; AND SO I DID NOT SEE WHEN I LOST SEPARATION. CONFLICT ALERT ACTIVATED AFTER THEY WERE LESS THAN 5 NM APART; AND THAT'S WHEN I TOOK EVASIVE ACTION TO SEPARATE THE 2 ACFT. I ISSUED BOTH ACFT 40 DEG TURNS; AND THEN ONCE THEY WERE SEPARATED BY MORE THAN 5 NM I TURNED THEM BACK ON COURSE. THE 2 ACFT CAME WITHIN 3.82 NM OF ONE ANOTHER. I OVERLOOKED ACFT Y AS HE WAS TRAVELING WBOUND DUE TO 1) HIS TARGET BEING COVERED BY ANOTHER DATA BLOCK; 2) THE COMPLEXITY OF THE TFC ON THE SCOPE; AND 3) BY BEING IN A HURRY IN WANTING TO GET THE ACFT X DOWN TO 10000 FT AND OUT OF THE WAY.