  Lists of equivalence classes of words under rotation or rotation plus
reversal (i.e., necklaces and bracelets) have many uses, and efficient
algorithms for generating these lists exist. In combinatorial group theory
elements of a group are typically written as words in the generators and their
inverses, and necklaces and bracelets correspond to conjugacy classes and
relators respectively. We present algorithms to generate lists of freely and
cyclically reduced necklaces and bracelets in free groups. Experimental
evidence suggests that these algorithms are CAT -- that is, they run in
constant amortized time.
