B757-200 LEFT ENG QUITS NEARING CRUISE ALT. DIVERTS TO NEAREST SUITABLE ARPT.

Narrative

APCHING FL330 FOR FL340; THE L ENG JUST QUIT. I CALLED FOR AND THE DRIFT-DOWN QRC WAS ACCOMPLISHED; ATC WAS NOTIFIED THAT WE NEEDED FL230; AN EMER WAS DECLARED; AND WE DIVERTED TO ZZZ1. BEING WE WERE NOT IN ETOPS AIRSPACE; I ELECTED TO FLY AT FL230 AND 270 KIAS VERSUS THE LOWER ETOPS ALT AND 310 KIAS. NO ATTEMPT WAS MADE TO RESTART THE ENG AS N2 AND OIL PRESSURE WERE ZERO AND N1 WAS SHOWING VERY LITTLE WIND-MILLING RPM. THE ENG WAS THEN SECURED. DISPATCH WAS NOTIFIED VIA ACARS AND FIRE EQUIP WAS REQUESTED. DECISION WAS MADE TO DIVERT TO ZZZ; DUE TO RAIN SHOWERS IN ZZZ2 AREA AS WELL THE FACT THAT THE ZZZ2 TWR WAS CLOSED. WITH R ENG OPERATING PROPERLY; THIS EXTRA TIME POSED NO THREAT TO THE CREW OR PAX BUT DID ALLOW TIME TO ORGANIZE THE CABIN AND MENTALLY PREPARE FOR A HVY WT (218.0) 20 DEG FLAP LNDG. THE LNDG WAS A NORMAL TOUCHDOWN. THE FLT ATTENDANTS WERE ADVISED AND TOLD THEY HAD 30 MIN TILL LNDG IN ZZZ; I MADE A QUICK PA ANNOUNCEMENT JUST AFTER THE ENG SHUT DOWN WITH THE FO MAKING A SLIGHTLY MORE DETAILED ONE 15 MIN BEFORE LNDG. THE FLT LANDED WITHOUT ANY FURTHER PROBS AND TAXIED TO THE GATE UNDER ITS OWN PWR.