ACR MLG ON VECTOR RWY 15 GOT GPWS WARNING ACCOUNT HIGH TERRAIN. CTLR ADVISED HAD ADEQUATE CLRNC. AGAIN VECTORED OFF THE APCH FOR SPACING AND GPWS WARNING; ELECTED TO CLB. ENDED UP HIGH ON APCH AND HAD TO MANEUVER TO MAKE THE APCH.

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ON RADAR VECTORS FOR LNDG RWY 15 AT BUR; ATIS RPTED CAVU; WINDS 150 DEGS AT 10 KTS. APCH WAS GIVING US RADAR VECTORS FOR THE STACKS VISUAL APCH; CLRED US TO 5000 FT; AND COMMENTED THAT HIGH TERRAIN AHEAD MAY GIVE US A GND PROX WARNING. THE GPWS SOUNDED AS WE CROSSED OVER THE HIGH TERRAIN ABOUT 1000 FT BELOW US. THEN THE CTLR TURNED US NE; AWAY FROM THE RWY; AND TOWARD MORE HIGH TERRAIN FOR SPACING ON ANOTHER AIRPLANE. I ASKED IF THIS WAS A SAFE ALT FOR THIS HDG; SINCE THE MOUNTAINS WERE DARK AND NOT READILY VISIBLE. SHE REPLIED IT WAS; AND EVENTUALLY TURNED US BACK TOWARD THE ARPT. AGAIN THE GPWS SOUNDED 'TERRAIN; TERRAIN' AND WE INITIATED A CLB AND ADVISED ATC. EVENTUALLY WE GOT THE ARPT BACK IN SIGHT; BUT WERE TOO CLOSE AND TOO HIGH; AND NEEDED TO MANEUVER TO LOSE ALT. AFTER TURNING AWAY FROM THE ARPT AND THE DISTRACTIONS WITH THE TERRAIN; IT WAS VERY DIFFICULT TO FIND THE RWY AGAIN. RECOMMENDATIONS: ATC SHOULD NOT VECTOR AN ACFT AT AN ALT WHERE THE GPWS WILL ISSUE A TERRAIN WARNING. USE HIGHER ALT! SECONDLY; WHEN 2 ACFT ARE APCHING THE SAME ARPT; DON'T VECTOR THE CLOSER ONE OUT OVER HIGH TERRAIN AT NIGHT. FINALLY; DME SHOULD BE AVAILABLE AT ALL ARPTS SERVING HIGH SPD JET ACRS. THANKS FOR YOUR EFFORTS IN AVIATION SAFETY.