A11 CTLR'S SEQUENCE AND SPACING RESULTED IN GAR WHEN SECOND ACFT; ON A VISUAL APCH; WAS TOO CLOSE TO FIRST LNDG ACFT.

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BOTH ACFT WERE ON VECTORS FOR THE SAME RWY. THE H/B777 WAS INBOUND FROM THE E; AND THE H/B744 WAS INBOUND FROM THE W. I VECTORED THE W ARR A LITTLE WIDE AND ISSUED A SPD RESTR OF 210 KTS ABOUT 25 MI W OF THE ARPT TO ALLOW THE H/B777 TO REMAIN #1 -- A SEQUENCING CALL I SHOULD HAVE LATER CHANGED. I HAD THE H/B777 ON A MODIFIED 8 MI DOWNWIND AND WHEN I BEGAN TO BASE HIM TO A NORMAL 6 MI FINAL; HE REQUESTED TO EXTEND ANOTHER MI AND A HALF. I FIGURED IT WOULD STILL WORK; SO I WIDENED THE H/B744 ANOTHER 20; SLOWED HIM TO 190 OR 180 BECAUSE HE WAS STILL SHOWING 290 ACROSS THE GND EVEN THOUGH I'D SLOWED HIM TO 210 KTS PREVIOUSLY. I TOLD THE H/B744 TO EXPECT A VECTOR ACROSS THE FINAL. I BASED THE H/B777 AND CLRED HIM FOR THE VISUAL APCH WITH A SPD ASSIGNMENT OF 180 KTS TO A 5 MI FINAL; SINCE I DIDN'T WANT HIM SLOWING FURTHER. TO THIS POINT IN MY SHIFT; EVERY ACFT HAD THEIR TFC AND THE FIELD IN SIGHT WITH NO DIFFICULTY -- SOME CALLING THE FIELD 50 MI OUT; SO I HAD NO INDICATION THAT THE H/B744 WOULD NOT CALL HIS TFC TO FOLLOW IN SIGHT. I POINTED OUT THE TFC TO FOLLOW AND HE SAID 'LOOKING.' I TURNED THE H/B744 R TO 110 TO GET BEHIND THE H/B777 AND WAITED UNTIL I HAD 4 MI BTWN THEM TO CLR HIM FOR APCH (ALL THIS TIME I HAD KEPT HIM 1000 FT OR MORE ABOVE THE H/B777). AFTER CLRING HIM FOR APCH; I ADVISED THE H/B744 TO SLOW TO 180 KTS OR LESS AND EXCHANGED TFC AGAIN; TO WHICH HE CALLED THE H/B777 IN SIGHT. THE H/B777 WAS ALREADY ON TWR FREQ BY THIS TIME AND WAS SLOWING SO I WAS CONCERNED ABOUT COMPRESSION BECAUSE OF RWY ACCEPTANCE. I TOLD THE TWR THAT THE H/B744 HAD THE TFC IN SIGHT AND FOLLOWING HIM; AND THE TWR ADVISED THE H/B777 WAS PREPPED FOR MINIMUM TIME ON RWY; SO I BELIEVED THE SEQUENCE WOULD WORK. IT WOULD BE CLOSE; BUT IT SHOULD WORK. THE H/B777 DID NOT MAKE THE HIGH-SPD DIAGONAL TXWY SO THE H/B744 WAS INSTRUCTED TO GO AROUND ON ABOUT A 3 MI FINAL. THERE WAS A CHAIN OF EVENTS HERE THAT I SHOULD HAVE RECOGNIZED AND BEEN MORE ATTENTIVE. FIRST AND FOREMOST; I CAME TO WORK SICK. I'VE BEEN SICK ALL WEEK AND NOT 100%. I AM FEELING 'BETTER' BUT NOT 'WELL.' STAFFING IS DEPLORABLE AND I WAS THE ONLY PERSON SCHEDULED ON THIS SHIFT UNTIL A SUPVR WAS CALLED IN ON OVERTIME TO WORK IT WITH ME. SECOND; NOT BEING WELL RESTED AND AS ALERT; I THOUGHT I COULD 'STUFF' THIS DOWNWIND IN AHEAD OF A STRAIGHT IN AND I JUST SHOULD NOT HAVE TRIED TO MAKE IT HAPPEN. ALL THINGS BEING EQUAL; THE SEQUENCE COULD HAVE GONE EITHER WAY; AND I CHOSE THE HARD WAY. I ALWAYS TELL MY TRAINEES THAT 'IF YOU VECTOR A GUY ACROSS THE LOC MORE THAN ONCE; YOU MADE A BAD SEQUENCE CALL' AND THOSE WORDS WERE RINGING IN MY EAR THIS WHOLE TIME. STILL; I STUBBORNLY CLUNG TO THE HOPE MY SEQUENCE WOULD WORK. THIRD; THE H/B744 PLT DID NOT SLOW AS ANTICIPATED/INSTRUCTED. HE LATER REFUSED TO CALL HIS TFC IN SIGHT UNTIL MY VERY NEXT XMISSION WAS TO CANCEL HIS APCH AND BREAK HIM OUT. HE WAS COMBATIVE ALL THE WAY IN. FOURTH; WHEN THE H/B777 REQUESTED TO EXTEND ONE MORE MI AND A HALF; I CONSIDERED BUT DID NOT CHANGE THE SEQUENCE THEN. I COULD HAVE EXTENDED HIM OUT TO BE #2 AND IT WOULD HAVE BEEN A NON-EVENT. I ALSO TRAIN MY TRAINEES THAT 'A STRAIGHT-IN BEATS A BASE; WHICH BEATS A DOWNWIND' WHEN DETERMINING A SEQUENCE ON FINAL. I SHOULD HAVE OBEYED THIS CREDO TOO AND MADE THE H/B744 #1 AND THIS WOULD HAVE BEEN A NON-EVENT. FIFTH; I SHOULD HAVE REQUESTED SOONER THAT THE H/B777 WAS FLYING A MUCH SLOWER FINAL APCH SPD INSIDE THE MARKER THAN THE H/B744 COULD AND BROKE #2 OUT INSTEAD OF GIVING HIM TO THE TWR; THINKING THE FIRST GUY WOULD BE OFF THE RWY IN TIME. SIXTH; I HAVE SEEN A SIMILAR SITUATION BEFORE WHEN I FIRST GOT HERE AT THIS FACILITY WHERE AN MD11 AND H/B747 GOT TOO CLOSE ON FINAL AFTER I'D VECTORED TRYING TO GET A DOWNWIND IN AHEAD OF A STRAIGHT IN. I KNEW BETTER THAN TO LET A CRAPPY SEQUENCE PLAY OUT THIS WAY; BUT I WAS NOT 100% AND THOUGH I WASN'T INATTENTIVE (I SAW IT WAS JUST NOT WORKING LIKE I WANTED) I DIDN'T WANT TO ADMIT IT WAS TOO CLOSE AND MAKE #2 FLY ANOTHER 8 OR 10 MI BY BOXING HIM AROUND DUE TO MY BAD CALL. IN THE END; HE HAD TO GO AROUND ANYWAY AND FLY BACK OUT TO A 8 MI FINAL COSTING HIM MORE THAN IT WOULD HAVE IF I'D HAVE JUST BROKE HIM OUT.