I have spoken several times with the owner of Kosrae Village Ecolodge in Micronesia.
His story is like many, in that a couple stuck in the corporate rat race buys a small piece of land in paradise and toils endlessly creating a nice dive resort in a slice of paradise somewhere...
Anyway, he said the proper pronunciation of Kosrae used by the natives is "Koosh-Eye". The oo sound is not like the oo in book, it is like the oo in pooh, as in Winnie the Pooh-Bear.
