A sentence refers to the pair of words which is complete in itself. In other words, a sentence contains a subject and a predicate or it may contain a main clause and one or more subordinate clauses to convey a command, exclamation, question or statement.
Subject refers to the doer of the action and predicate is the action performed.
Hence, when we notice in the above sentence, 'fit' is the verb which acts as a simple predicate and 'small mice' are the subject.
To determine the complete predicate, it answers,
The small mice fit where?- into coat pockets, as a result, the complete predicate is 'fit nicely into coat pockets.'