AN ACR ACFT IS TOLD TO HURRY BACK DOWN TO FL280 WHEN AT FL300 CLBING DUE TO TFC AT FL290; OPPOSITE DIRECTION TFC.

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CRUISING AT FL280; TALKING TO ZME (FREQ 132.42; SECTOR 21). REQUESTED CLB TO FL350. CTR CLRED ME TO FL310. DURING CLB; AT APPROX FL300; CTR ASKED US TO 'DSND TO FL280; HURRY DOWN.' WE BEGAN TO DSND; AND RECEIVED A TCASII RA TO DSND. WE FOLLOWED THE RA; THEN VISUALLY ACQUIRED THE OTHER ACFT; WHICH APPEARED TO BE AT FL290. I HESITATED TO CONTINUE FOLLOWING THE RA; AS IT APPEARED I WOULD DSND THROUGH THE INTRUDER'S ALT AT POSSIBLY VERY CLOSE RANGE. AS THE DISTANCE/MOTION SIT EVOLVED; IT APPEARED THAT THE RA DSCNT COULD BE COMPLETED SAFELY; AND WE EXPEDITED DSCNT THROUGH FL290 TO FL280. INTRUDER PASSED 1000 FT OVERHEAD; AT APPROX 1/2 MI LATERAL SEPARATION. INTRUDER ASKED ATC TO VERIFY 'CLRED TO FL310.' DURING DSCNT; REACHED FL277 UNTIL 'CLR OF CONFLICT' ANNOUNCED; THEN MAINTAINED FL280. MY HESITATION DURING THE DSCNT STEMS FROM A RELUCTANCE TO DSND THROUGH THE ALT OF A VISUALLY ACQUIRED ACFT IN CLOSE PROX. IF IN FACT THE INTRUDER WAS LEVEL AT FL290; AND HADN'T STARTED TO CLB TO FL310; IT SEEMED AN UNNECESSARY RISK TO DSND THROUGH HIS ALT; RATHER THAN CONTINUE OUR CLB THROUGH FL300 TO FL310. THE LESSON HERE FOR ME IS THAT THE TCASII GUIDANCE IS INVALUABLE; BUT IS COMPLICATED WHEN VISUAL ACQUISITION APPEARS TO CONFLICT WITH TCASII GUIDANCE. SUPPLEMENTAL INFO FROM ACN 436803: ATC PROVIDED INACCURATE PHONE NUMBER TO CONTACT -- UNABLE TO DETERMINE FAULT OR MISTAKE. ANOTHER COMPANY FLT REQUESTED CONFIRMATION THAT IT WAS CLRED TO FL310.