  Good words are binary words avoiding factors 11 and 1001, and patterns 0000
and 00010100. We show that good words bear the same relationship to the
period-doubling sequence that overlap-free words bear to the Thue-Morse
sequence. We prove an analogue of Fife's Theorem for good words, exhibit the
lexicographically least and greatest infinite good words, and determine the
patterns avoided by the period doubling word.
