ACR X TCASII TA DSCNT TO OCCUPIED ALT HAD LTSS FROM ACR Y. SYS ERROR.

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ON J80 WBOUND AT FL310; THE RIDE BECAME BUMPY AT THIS ALT SO THE PF ASKED ME TO REQUEST LOWER ALT. UPON OUR REQUEST; ZOB ASKED US TO STAND BY A MOMENT; THEN HE ISSUED US DSCNT CLRNC TO FL280. JUST PRIOR TO LEVELING AT FL280; THE TCASII ISSUED A TA. WE OBSERVED A TARGET ON THE TCASII SCREEN AT OUR 2 O'CLOCK POS; CLBING FROM 600 FT BELOW US AND CONVERGING. WE QUESTIONED ATC AS TO THE TFC PRESENCE AND HE IMMEDIATELY ISSUED AN IMMEDIATE 90 DEG L TURN. AT NO TIME DID WE ALTER OUR COURSE TO AVOID THE CONFLICT EITHER FROM A RADAR VECTOR OR AN RA FROM THE TCASII. THE CLOSEST THE 2 ACFT GOT APPEARED ON THE TCASII TO BE 4 MI HORIZ AND CO-ALT CONVERGING AT 90 DEGS. THE CAPT CALLED TO ASK ATC HOW SUCH A SIT HAD OCCURRED. THE CTLR INDICATED THAT HE HAD SET UP OUR DSCNT SO AS TO CROSS IN FRONT OF THE CLBING TFC WITH THE PROPER VERT SEPARATION BASED ON HIS ESTIMATE OF WINDS AND EACH ACFT'S SPD. HE ALSO INDICATED THAT HE BECAME UNAWARE THAT WE WERE GOING TO PASS SO CLOSE. IN HIS ATTEMPT TO ACCOMMODATE OUR REQUEST FOR A LOWER ALT; HE SET UP A PROX CONSTRAINT WHICH WORKED OUT JUST A BIT TOO CLOSE. IF WE HAD BEEN IN A NON TCASII ACFT AND HAD NOT OURSELVES BECOME AWARE OF THE TFC; THE 2 ACFT COULD HAVE PASSED MUCH; MUCH CLOSER GIVEN THE CTLR'S DISTR. THE TCASII ALERTED US TO THE CONVERGENCE WITH ENOUGH TIME TO QUERY THE CTLR WHICH ALLOWED HIM TO REACT.