A SF34 DSNDING INTO SPS CAME WITHIN AN ESTIMATED 300 FT VERTLY AND LESS THAN 750 FT HORIZ OF A CESSNA 500 DEPARTING VFR. THE CESSNA WAS RPTED TO HAVE THE SF34 IN SIGHT BY SPS TRACON.

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THIS RPT IS ABOUT A FLT; DFW TO LAW. CLRED TO 6000 FT FROM 12000 FT; WE WERE DSNDING AT ABOUT 1000 FPM WHEN WE GOT A TCASII TA ALERT ON TFC AT LESS THAN 10 MI AND OUR 11:30 O'CLOCK POS. THE TA ALERT QUICKLY BECAME AN RA AND DIRECTED US TO CLB AT A RATE GREATER THAN 2500 FPM. THE RA COMMAND DID NOT CALL FOR LEVELOFF UNTIL WE WERE CLBING THROUGH 10200 FT MSL. SHEPPARD APCH WAS NOTIFIED OF OUR DEV AS SOON AS PRACTICABLE. ALTHOUGH WE HEARD THE TFC; A C500 BIZJET CHKED ON; CLBING OFF OF THE KICKAPOO DOWNTOWN ARPT. APCH MADE NO MENTION OF THE CONFLICT UNTIL WE STARTED DEVS. LOCATION OF THE EVENT WAS 43 NM S OF LAW ON THE 175 DEG RADIAL. MINIMUM SEPARATION DURING THE EVENT WAS ABOUT 300 FT VERT AND LESS THAN 1/8 MI HORIZ. SHEPPARD APCH DESCRIBED THE TFC AS VFR AND RPTED THAT THEY HAD CALLED US 'IN SIGHT.' SPS METAR; 0210KT; 5 MI IN HAZE; SCATTERED 013; BROKEN 250; 04/MI; ALTIMETER 30.41. I BELIEVE THE C500 MAY HAVE PICKED UP AN IFR CLRNC AFTER WE LEFT THE FREQ. WE NEVER HAD THE TFC IN SIGHT; PROBABLY DUE TO OUR PITCH ATTITUDE DURING THE AVOIDANCE MANEUVER. EITHER SPS APCH NEEDS TO REEVALUATE THEIR OPS OR WE NEED TO CONSIDER ANOTHER ALTERNATIVE FOR THIS EVENT. WITHOUT THE TCASII SYS SURELY THIS WOULD HAVE BEEN A DIFFERENT TYPE OF EVENT.