BOTH LEFT TIRES FAIL AFTER LNDG.

Narrative

I WAS FLYING FROM LGB-SFO. AFTER A LONG TAXI OUT (8000') WITH A LIGHT ACFT (67000 LBS); WE HAD TO MAKE A LOW SPD REJECTED TKOF DUE TO CONFLICTING HELI TFC DOWNFIELD. WE LET IT ROLL OUT (ABOUT 8000') AND THEN TAXIED BACK FOR TKOF (ABOUT 8000') AND MADE A NORMAL TKOF. BECAUSE OF OUR LIGHT WT; CONTINUAL TAPPING OF THE BRAKES WAS REQUIRED TO KEEP OUR TAXI SPD DOWN. UPON LNDG AT SFO AFTER A NORMAL T/D; A VIBRATION WAS FELT IN THE ACFT AS THE LIFT SPOILERS WERE EXTENDED AND IT VEERED TO THE LEFT. I WAS ABLE TO CONTROL THE ACFT AND GET IT OFF THE RWY AT THE HI SPD TURNOFF. TWR ADVISED WE HAD 'SMOKE FROM THE LEFT BRAKES;' SO WE ORDERED CRASH EQUIP; STAND BY. FORTUNATELY THERE WAS NO FIRE AND WE DID NOT DO AN EMER EVAC. INSPECTION OF THE LEFT GEAR AFTERWARDS REVEALED BOTH TIRES HAD BLOWN; THE #1 TIRE HAD SHREDDED BUT THE #2 TIRE WAS STILL ON THE RIM. MAINT SEEMED TO FEEL THE FUSE PLUGS ON #1 HAD LET GO ENRTE DUE TO OVERHEATED BRAKES AND THE #2 TIRE FAILED AFTER THE T/D. IT IS INTERESTING TO NOTE THAT EVEN AFTER EXTENSIVE WORK ON THE BRAKES; THE FIRST FLT OF THIS ACFT AFTERWARDS RESULTED IN 'HOT LEFT BRAKES; COOL RIGHT BRAKES AFTER LIGHT BRAKING' WRITE UP. A SECOND QUESTION RELATES TO THE QUALITY OF THE RECAPS WE ARE NOW USING--HOW ARE THEY TESTED? WHY DID #2 TIRE FAIL? IT SHOULD HAVE BEEN ABLE TO HOLD THE LOAD. AND FINALLY; SHOULD WE DO SOME TESTING RE: THE DANGERS INVOLVED IN TAXIING LIGHT ACFT OVER LONGER THAN NORMAL DISTANCES? ANY OR ALL OF THE FACTORS MAY HAVE BEEN INVOLVED IN THIS INCIDENT.