AIR TAXI CARGO ACFT TOLD HAD CLOSE PROX WITH ACR AT LEVEL OFF AFTER RAPID DSCNT. TCASII.

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ENRTE FROM DFW TO DET AT FL410. WE WERE GOING DIRECT TO FWA VOR TO JOIN V11 TO THE CRUXX INTXN. WE REQUESTED TO DEVIATE E OF COURSE TO AVOID SOME BUILDUPS THAT WERE IN THE FORT WAYNE AREA. APPROX 70 NM S OF FWA CHICAGO CENTER TOLD US TO DSND TO FL240 ABEAM FWA VOR. WE REPLIED THAT WE WOULD LIKE TO REMAIN AT FL410 A LITTLE LONGER TO VISUALLY AVOID THE BUILDUPS AND COULD GIVE HIM A GOOD RATE DOWN IN THE DSCNT. HE APPROVED THIS AND TOLD US TO NOTIFY HIM WHEN WE LEFT FL410. I TOLD THE FO; WHO WAS FLYING; TO REDUCE THE PWR AND SLOW THE ACFT; SO WE COULD MAKE A QUICK DSCNT. AFTER STARTING OUR DSCNT WE WERE TOLD TO MAINTAIN FL370 INSTEAD OF FL240. I REPLIED THAT THAT WAS NO PROBLEM. WE STILL WANTED TO GIVE ATC A GOOD RATE TO FL370 AND PUSHED THE PLANE OVER TO ACHIEVE A HIGH RATE OF DSCNT. UPON REACHING FL370 I TOOK CTL FROM THE FO FOR THE LEVEL OFF WHICH REQUIRED CONSIDERABLE FORCE. A FEW MOMENTS LATER AN AIRLINES FLT CALLED CENTER AND SAID THAT ACCORDING TO THEIR TCASII SYS IT INDICATED WE WERE WITHIN 400 FT OF THEM; HOWEVER THEY DIDN'T TAKE ANY EVASIVE ACTION. ATC ASKED OUR ALT; WE REPLIED FL370 AND SAID THAT WAS WHERE WE LEVELED OFF. ATC THEN GAVE US A TELEPHONE NUMBER TO CALL. UPON RETURNING I INFORMED MAINT WHO FOUND THE TRANSPONDER FAULTY AND THE ENCODING ALTIMETER. I CAN ONLY GUESS THAT THE GREAT RATE OF DSCNT AND ABRUPT LEVEL OFF MAY HAVE RESULTED IN INACCURATE INFO TO BE INDICATED BY ATC AND ACR. IN THE FUTURE MORE REASONABLE RATES OF DSCNT WILL BE USED TO AVOID THIS PROBLEM.