FLC OF AN ACR MLG ACFT OVERSHOT DSCNT ALT RESULTING IN A TCASII RA.

Narrative

WE WERE GIVEN AN EARLY DSCNT CLRNC BY CTR TO 'CROSS JULLE AT OR BELOW 12000 FT; MAINTAIN 12000 FT.' (NORMAL CLRNC IS TO CROSS JULLE AT OR BELOW 14000 FT; MAINTAIN 10000 FT.) THIS CLRNC WAS REVISED TO 'CROSS JULLE AT OR BELOW 11000 FT; MAINTAIN 10000 FT.' PASSING 12600 FT; CTR ASKED OUR ALT; THEN GAVE US 240 DEG HDG (WE WERE TRACKING 278 DEG RADIAL LNY) AND EXPEDITE DSCNT. WE WERE THEN GIVEN 280 DEG HDG AND TOLD TO CONTACT APCH. FO WAS FLYING AND SANK THROUGH 10000 FT TO 9700 FT ON LEVEL OFF. I TOLD HIM TO GET BACK TO 10000 FT IMMEDIATELY. AT THIS EXACT TIME; WE GOT AN RA ON TCASII TO 'CLB' WHICH CEASED AS WE LEVELED AT 10000 FT. WE SIGHTED OPPOSITE DIRECTION TFC AS I CHKED IN WITH APCH. TFC WAS BELOW US AT 9000 FT; PASSED 3 MI OFF TO R. WE WERE NEVER ADVISED OF TFC OR THE REASON FOR AN EXPEDITED DSCNT; APPARENTLY INTO A POTENTIAL CONFLICT. CORRECTIVE ACTIONS: IF AT ALL POSSIBLE; ATC SHOULD ADVISE CREW OF REASON FOR EXPEDITED ACTION. CONTRIBUTING FACTORS: EXPEDITED ACTIONS MAY LEAD TO EXCURSIONS WHEN CREW IS SEARCHING FOR TFC.