B777-200 CREW HAD A TCASII RA WITH A PIPER ACFT JUST ABOVE DFW CLASS B.

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LEVEL 10000 FT APPROX 20 NM W OF DFW NBOUND AFTER RWY 18L DEP. WE WERE CLRED TO 12000 FT. IN CLB; ATC NOTIFIED US OF TFC 12:30 O'CLOCK POS; LESS THAN 5 NM AT 12500 FT VFR WBOUND PIPER. DID NOT HAVE VISUAL. RECEIVED TA ON TCASII THEN PASSING 11600 FT RECEIVED RA WITH AN AUDIO DSND. AUTOPLT WAS OFF AND I PROMPTLY RESPONDED AS CAPT STATED PROCS. SECONDS LATER; A PIPER WENT DIRECTLY OVERHEAD AT 1000 FT ABOVE US AS INDICATED BY TCASII. (IT LOOKED CLOSER AND I WONDER WHAT WE LOOKED LIKE TO HIM!) EVEN THOUGH 500 FT WAS LEGAL SEPARATION AS PROVIDED BY ATC; THE TCASII DSNDED US TO 1000 FT BELOW CONFLICTING TFC. GIVEN THE MASS AND ACCELERATION AND CLB RATE OF A LIGHT B777; 500 FT IS NOT ENOUGH SPACE TO LEVEL COMFORTABLY BELOW A LIGHT VFR ACFT. WE WOULD HAVE PREFERRED TO STAY AT 10000 FT OR 11000 FT. KUDOS TO ATC REGARDLESS; THEY DID EVERYTHING BY THE BOOK; BUT 500 FT IS TOO LITTLE SEPARATION IN THIS CASE. SPECIAL THANKS TO TCASII SOFTWARE THAT INSTRUCTED US TO MAINTAIN AT LEAST 1000 FT OF SEPARATION. AND NOT TO HAVE TO MANEUVER LIKE THAT.