FLC OF AN ACR HVT OVERSHOT ASSIGNED CLB ALT RESULTING IN A LTSS WITH ANOTHER ACFT IN THE OPPOSITE DIRECTION.

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SHORTLY AFTER TKOF OUT OF DALLAS (DFW) ACR X FLT WAS ON THE WAY UP TO AN ASSIGNED ALT OF 10000 FT. THE CONDITIONS THAT DAY WERE CLR; VFR; WITH SCATTERED CUMULUS CLOUDS IN THE AREA. DURING OUR CLBOUT CTR DIRECTED OUR ATTN TO NUMEROUS TFC TARGETS IN THE AREA; THEREFORE ALL 3 CREW MEMBERS WERE LOOKING OUT FOR TFC AND POINTING OUT TO EACH OTHER WHAT THEY THOUGHT WERE THE VARIOUS TARGETS. I RECALL WE HAD SOME DIFFICULTY RECONCILING ONE TARGET AND THIS DIVERTED A CONSIDERABLE AMOUNT OF OUR ATTN. THUS; IN THE PROCESS OF TRYING TO BE VIGILANT IN OUR CLB WITH RESPECT TO TFC; OUR ALT WAS MOMENTARILY EXCEEDED. HOWEVER; WE REALIZED WHAT HAD HAPPENED VERY QUICKLY AND WERE IN THE PROCESS OF EXPEDITING BACK DOWN WHEN CTR ALERTED US. REFLECTING BACK AFTERWARDS; WE FOUND THAT THE ALT ALERTER ON THE ACFT IS SO QUIET THAT IT IS ONLY AUDIBLE IN A PERFECTLY QUIET COCKPIT; AND A DC-8 AFTER TKOF HAS EXTREMELY HIGH LEVELS OF COCKPIT NOISE. ALSO; NEITHER THE FE NOR MYSELF WAS ABLE TO HEAR THE '1000 FT TO GO' CALLOUT FROM THE CAPT. IN THE FUTURE; I AM GOING TO STRONGLY SUGGEST TO THE CAPTS THAT ANY 'QUIET' ALT ALERTERS BE WRITTEN UP FOR ADJUSTMENT EVEN THOUGH THEY AREN'T 'BROKEN.' ALSO; I THINK IT IS GOOD PRACTICE TO HAVE THE PF VERBALLY RECOGNIZE THE CALLOUTS OF THE PNF TO MAKE SURE HE IS AWARE OF WHAT WAS SAID -- ESPECIALLY IN A NOISY COCKPIT WHERE COM IS DIFFICULT. SUPPLEMENTAL INFO FROM ACN 273752: CREW PREOCCUPIED LOOKING FOR TFC OUTSIDE OF THE COCKPIT FOR A PROLONGED PERIOD. PF ABANDONING SOME OF HIS DUTIES TO LOOK FOR TFC. NOT GETTING ATC ADVISORIES WHEN TFC IS NO LONGER A FACTOR IF WE DIDN'T LOCATE TFC. POOR DELEGATION OF DUTIES IN THIS SIT AND A GENERAL CREW ERROR. SUPPLEMENTAL INFO FROM ACN 273174: ACFT RPTED ON FREQ DID NOT STATE CURRENT OR ASSIGNED ALT. I REISSUED 'MAINTAIN 10000 FT.' AT APPROX 8000 FT I ISSUED 'TFC 1 O'CLOCK; 8 MI; NEBOUND; 11000 FT.' THE PLT STATED 'LOOKING.' SEVERAL SECONDS LATER ANOTHER CTLR ALERTED ME THAT THE ACFT HAD BUSTED HIS ALT. I OBSERVED HIM CLBING OUT OF 10400 FT AND ISSUED AN IMMEDIATE DSCNT TO 10000 FT. THIS ACFT WAS NOT TCASII EQUIPPED. THE 11000 FT TFC HAD ALREADY RECEIVED AN RA AND BEGAN A DSCNT TO 10000 FT WHICH CREATED AN IMMINENT CONFLICT WITH A SECOND DEP CLBING TO 10000 FT. THE SECOND ACFT RECEIVED AN RA AND WE WERE ABLE TO STOP HIS CLB AT 9000 FT. ONE THING THAT CONCERNS ME GREATLY IS THAT YOU CANNOT HAVE A COORDINATED RESOLUTION WITH ONLY 1 PARTICIPANT. IF I HAD SEEN THE DEV A LITTLE SOONER AND ACTUALLY DSNDED THE NON TCASII ACFT BACK TO 10000 FT; THEN THERE MIGHT HAVE BEEN A CTLED COLLISION; BOTH ACFT DOING WHAT THEY WERE TOLD -- 1 BY TCASII; AND 1 BY ME. AS IT WAS; THE TCASII ACFT WAS ABLE TO DSND BELOW THE DEVIATING ACFT.