A B757-200 OVER THE OCEAN EXPERIENCES AN ENG FAILURE. THE FLT CREW SHUTS DOWN THE ENG; DECLARES AN EMER; AND LANDS AT THE ARPT BEST EQUIPPED TO HANDLE THE ACFT.

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HOW TO PROB AROSE: SHUT DOWN R ENG DUE TO FLUCTUATING N3 AND PNEUMATIC SURGES. HOW IT WAS DISCOVERED: FO OBSERVED AND BROUGHT IT TO MY ATTN. CORRECTIVE ACTIONS: COMMANDED COMPLETION OF THE ENG SHUTDOWN CHKLIST; DSNDED TO SINGLE ENG ALT; DECLARED AN EMER; REQUESTED DIRECT ROUTING TO ZZZ. CONTRIBUTING FACTORS: PROX TO ETOPS EXIT POINT (PAST IT AND COASTING IN TO ZZZ AIRSPACE). PROX TO ETOPS ENRTE ALTERNATE. HUMAN PERFORMANCE CONSIDERATIONS -- PERCEPTIONS/JUDGEMENTS/DECISIONS: WITH GIVEN INDICATIONS AND LACK OF A DEFINITIVE CHKLIST TO REF; THE SITUATION WARRANTED A PRECAUTIONARY SHUTDOWN TO PREVENT FURTHER DAMAGE OR RISK A POSSIBLE CATASTROPHIC FAILURE. LNDG PERFORMANCE SUPPORTED BOTH RWYS. THE DECISION TO ELECT ZZZ ARPT IN LIEU OF THE CLOSER ZZZ1 ARPT; ZZZ WAS ONLY ANOTHER APPROX 7 MINS FLYING TIME; RWY LENGTH; MORE CFR; MEDICAL SUPPORT IF NEEDED; FAMILIARITY WITH THE ARPT AND GEOGRAPHICAL LAYOUT DUE TO MULTIPLE OP IN AND OUT OF ZZZ; THE ABILITY TO RESTART THE ENG IF IN MY JUDGEMENT ITS START WAS REQUIRED FOR SAFETY OF FLT. FACTORS AFFECTING HUMAN PERFORMANCE: HAD I BEEN WITHIN ETOPS AIRSPACE WHEN DECLARING AN EMER; I WOULD HAVE BEEN BOUND BY COMPANY DIRECTIVE AND FAR TO DIVERT TO MY ETOPS ENRTE ALTERNATE; WHICH HAD REQUIRED CFR; HOWEVER; THE RWY WAS MUCH SHORTER AND THE ARPT WX TENDS TO BE MORE VOLATILE THAN ZZZ. A RECIPE FOR A POSSIBLE MISHAP UNLESS THE PIC WERE TO EXERCISE EMER AUTH AND DIVERT TO ZZZ AND THEN FIND THEMSELVES UNDER EXTREME SCRUTINY FOR MAKING THAT DECISION.