FLC OF AN MLG ACR ACFT DSNDED BELOW ASSIGNED CRUISE ALT IN RESPONSE TO A TCASII RA.

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WHILE AT CRUISE FLT AT FL280 ON RADAR VECTORS FOR TULSA; I RECEIVED AN RA ON TCASII AND IMMEDIATELY FOLLOWED IT AS PER COMPANY PROC. I DSNDED TO 27500 FT BEFORE RECEIVING A 'CLR OF CONFLICT' AND RETURNING TO FL280. THE INTRUDER WAS AT FL290 ALSO IN CRUISE FLT; HDG THE OPPOSITE DIRECTION. THE CTLR; WHO WAS UNDERSTANDABLY QUITE UPSET; INFORMED ME AFTERWARDS THAT I HAD CONFLICTING TFC AT FL260. HE ALSO INFORMED ME THAT I WAS OVER A REFUELING RTE WHERE THE BLOCK ALTS ARE FL250-270. THE CTLR WAS VERY BUSY AND DID NOT CALL OUT THE INTRUDER PRIOR TO MY RA. I FELT LIKE THIS RA WAS UNNECESSARY; BUT OUR COMPANY PROCS DIRECT US TO FOLLOW ALL RA'S UNLESS WE ARE IN DANGER OF HITTING ANOTHER ACFT. I DID NOT ACQUIRE THIS INTRUDER VISUALLY UNTIL AFTER THE RA. THE TCASII SHOWED WE WERE WITHIN 700 FT AND 3-4 MI AT THE CLOSEST POINT. THE TCASII GIVES MANY TA'S AND RA'S IN THE ARR AND DEP CORRIDORS WHICH ARE QUITE ANNOYING. INCIDENTS LIKE THIS ONE IN AREAS OF POSITIVE CTL DO NOT BUILD CONFIDENCE IN THE EQUIP AND HAVE A REAL POTENTIAL FOR DISASTER. THIS TCASII SYS HAS A LONG WAY TO GO BEFORE IT IS SAFE TO FOLLOW BLINDLY AS OUR COMPANY PROCS DICTATE.