Fish is great. Also the Bridport Prize and the Poetry Society awards are also prestigious. But don't forget your more regional and local comps - always good to get on your CV too. Good luck!
Fish and Bridport are prestigious and fiercely competitive. Leaf Books run them, and Mslexia magazine has excellent listings of local and national competitions, and also calls for submission to poetry mags. You don't have to subscribe - libraries have it.
Emma
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You could also browse through the Members' Successes pages here on WW for ideas, as members have done well in all sorts of competitions from tiny to huge.
Peterloo Poets, who are an importatnt poetry publisher, have just announced their competition. Many if not most comps are listed in Jobs and Opps here on WW, too.