Which word best completes the sentence to mean 'cabin'?

For example, the sentence "Im Wald gab es eine kleine Hütte, in der ein alter Mann lebte."

In this sentence, 'Hütte' is the correct term to use in German to denote a 'cabin', 'hut', or 'cottage'. 'Hütt' doesn't exist in German, 'Hütten' would be the correct plural form, and 'Hüte' translates to 'hats', which doesn't make sense in this context.