CAPT OF AN MLG INCREASED THE RATE OF CLB IN RESPONSE TO OBSERVATION OF A CONFLICTING TFC; TCASII AND AN ATC ADVISORY.

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CTR POINTED OUT TFC WHICH WE FOUND ON TCASII AND ACQUIRED VISUALLY. CTR CLRED US TO CLB PAST THE VFR SMALL PLANE; AND WE DID SO; TURNING INTO IT SLIGHTLY TO COMPLY WITH THE SID. WE HAD A GOOD RATE OF CLB GOING WHEN THE TCASII DIRECTED US TO DSND IMMEDIATELY. THERE WAS NO WAY TO DSND WITHOUT CLBING THROUGH THE VFR ACFT'S ALT ANYWAY; (ESPECIALLY CONSIDERING THE PEOPLE IN THE CABIN) SO I INCREASED THE RATE OF CLB INSTEAD TO MINIMIZE TIME AT TARGET'S ALT. SAFETY WAS NOT COMPROMISED SINCE I KEPT THE OTHER ACFT IN SIGHT AND THE MISS DISTANCE WAS ABOUT 1000 FT AS I PASSED THROUGH ITS ALT. ALTHOUGH I AM A PROPONENT OF TCASII; I MUST COMMENT THAT IT APPEARS TO BE PROGRAMMED WITHOUT RESPECT TO ACFT CAPABILITY. MY BEST JUDGEMENT TOLD ME TO DO JUST THE OPPOSITE OF THE TCASII COMMAND; EVEN KNOWING THAT THE OTHER ACFT MIGHT BE RESPONDING TO HIS TCASII AND MY ACTIONS MIGHT BE THWARTING THE COORD BTWN SYS. OF COURSE; IN IMC CONDITIONS I WOULD HAVE FOLLOWED THE TCASII COMMANDS; BUT IT IS SCARY TO KNOW THAT IT MIGHT ACTUALLY INCREASE EXPOSURE TO MID-AIR RISK.