  We enumerate all ternary length-l square-free words, which are words avoiding
squares of words up to length l, for l<=24. We analyse the singular behaviour
of the corresponding generating functions. This leads to new upper entropy
bounds for ternary square-free words. We then consider ternary square-free
words with fixed letter densities, thereby proving exponential growth for
certain ensembles with various letter densities. We derive consequences for the
free energy and entropy of ternary square-free words.
