CAPT OF A B737-300 OVERSHOT ASSIGNED ALT DURING DSCNT FOR APCH DUE DISTR FROM AN EARLIER TCASII ALERT. CTLR INTERVENED AND ISSUED CLRNC.

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BEING VECTORED FOR APCH TO DIA; RWY CHANGE FROM RWY 35L TO RWY 7. WAS GIVEN CLRNC FROM 15000 FT TO 13000 FT AND R TURN TO 190 DEG HDG. THEN L TURN TO 170 DEGS TO FOLLOW TFC TO RWY 7. TFC AHEAD WAS AT 11000 FT AND WAS ABOUT 6 MI AHEAD ON TCASII. WE BEGAN TO TRY AND VISUALLY ACQUIRE TFC AND BE READY FOR VISUAL APCH. AT THAT TIME GOT ALT ALERT AND IMMEDIATELY STOPPED DSCNT AT 12700 FT AND BEGAN CLB BACK TO 13000 FT. FO POINTED TO ALT SELECT SET AT 13000 FT. SIMULTANEOUSLY; APCH GAVE CLRNC TO 8000 FT AND WE THEN CONTINUED DSCNT AND LNDG AT DIA RWY 7. NO CONFLICT OR SEPARATION WAS LOST WITH OTHER TFC AND ATC DID NOT MENTION ALTDEV. AS CAPT; I ALLOWED MYSELF TO GET DISTR FROM COMPLYING WITH CLRNC; BY ANTICIPATING A CLRNC LOWER AS OTHER AIRPLANE AHEAD HAD RECEIVED AND BY LOOKING OUTSIDE FOR TFC TO FOLLOW IN PREPARATION FOR VISUAL APCH. ALTHOUGH IT IS IMPORTANT TO BE READY FOR NEXT CLRNC; THE FIRST PRIORITY SHOULD HAVE BEEN WITH FOLLOWING THE CURRENT CLRNC. NO EXCUSES AND A HARD LESSON WELL LEARNED.