ARTCC RADAR CTLR DSNDED A CORPORATE MLG TO FL350 FROM FL450 AND THEN SAW HE WOULD BE IN CONFLICT WITH AN ACFT AT FL370 AND TRIED TO STOP THE MLG AT FL390. DUE TO AN INCREASED DSCNT RATE; THE MLG OVERSHOT TO FL371 AND RECEIVED A TCASII TA ON THE TFC.

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ENRTE FROM SAN TO PHL AT FL450; CTR CLRED US TO FL410. AS WE WERE LEVELING; FURTHER DSCNT CLRNC TO FL350 WAS ISSUED. PASSING FL400; HE REQUESTED US TO EXPEDITE DSCNT. RATE WAS INCREASED FROM 2000 FPM TO 3000 FPM. PASSING FL380; WE WERE TOLD TO LEVEL AT FL390. FO ADVISED HIM OF OUR PASSING ALT AND ASKED IF WE SHOULD CLB. CTLR TOLD US TO CLB TO FL390 AND TURN L TO A 360 DEG HDG (AIRWAY IS EBOUND). DSCNT WAS ARRESTED AT FL371 AND CLBING TURN INITIATED. TCASII TA INDICATED TFC 100 FT BELOW US; PASSING OFF OUR R. TCASII RANGE WAS SET AT 40 MI; SO IT SHOWED US ALMOST OVER TARGET. I SUSPECT IT WAS 1-2 MI LATERALLY. WE DIDN'T SEE THE OTHER ACFT. WE WERE AWARE OF AN 'OPERATIONAL SIT' BASED ON CTR'S INSTRUCTIONS. WHEN HE INITIATED THE CLB (TO FL390) INSTRUCTION; I SHOULD HAVE MORE FORCEFULLY CHANGED OUR VERT PROFILE; RATHER THAN LETTING SMOOTHNESS ENDANGER LIVES. ADDITIONAL TCASII NOTE: THE OTHER ACFT'S READOUT ON OUR TCASII WAS NOTED AT APPROX 25 MI. AT SOME POINT IT DISAPPEARED FOR A SIGNIFICANT PERIOD BEFORE POPPING BACK UP -- AS A TA! (I SUSPECT HE WAS CHANGING BEACON CODES.)