NMAC BTWN A CESSNA CITATION; CE560; DSNDING THROUGH 6500 FT 42 MI FROM LIT AND A C172 IN LEVEL FLT. THE RPTING CITATION INCREASED RATE OF DSCNT TO ASSURE SEPARATION.

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AFTER BEING TURNED OVER TO LIT APCH FROM ZME AT AN ALT OF 9000 FT MSL; WE WERE GIVEN A VECTOR AND DSCNT TO 5000 FT MSL. AROUND 7000 FT MSL WE HAD A TCASII TFC ALERT AT 1400 FT BELOW US. THE DSCNT WAS SLOWED AND AT THE SAME TIME LIT APCH CALLED TFC 12 O'CLOCK PRIMARY TARGET ONLY. WE SAW THE TFC AT OUR ALT AND TOOK EVASIVE ACTION TO AVOID. THE C172 PASSED ABOUT 200 FT ABOVE OUR ACFT. SUPPLEMENTAL INFO FROM ACN 467839: IN CONCLUSION; MY PERSONAL OPINION IS THAT OUR HANDLING BY ZME TO DSND US LOWER IN ORDER TO EXPEDITE THE HANDLING OF THE ACR Y FLT BEHIND US WAS A CONTRIBUTING FACTOR IN THAT IT DSNDED US LOWER FARTHER OUT (57 NM) THAN WE SHOULD HAVE BEEN AT THAT POINT DURING TRANSITION INTO LIT. THIS RESULTED IN LIT APCH DSNDING US INTO THE LOWER ALTS OF CLASS E AIRSPACE MUCH FARTHER FROM LIT THAN WHAT WE SHOULD HAVE BEEN AT THAT POINT DURING THE FLT. WE WERE DSNDED INTO CLASS E AIRSPACE ALTS GENERALLY USED BY SLOWER; LOWER FLYING ACFT WHERE NO ALT RPTING IS REQUIRED FOR VFR FLT BELOW 10000 FT. HAD MEMPHIS GIVEN US OR ACR Y -- OR BOTH -- A TURN TO AVOID ARR CONGESTION INTO LIT; WE BOTH COULD HAVE CROSSED AT 35 NM AND 10000 FT OUT FROM LIT. THE SAFE HANDLING OF ACFT SHOULD BE OF THE UTMOST IMPORTANCE; REGARDLESS OF SIZE OF SPD. THIS FLT ALMOST COST MYSELF AND OTHERS THEIR LIVES.