  A $4^-$-power is a non-empty word of the form $XXXX^-$, where $X^-$ is
obtained from $X$ by erasing the last letter. A binary word is called {\em
faux-bonacci} if it contains no $4^-$-powers, and no factor 11. We show that
faux-bonacci words bear the same relationship to the Fibonacci morphism that
overlap-free words bear to the Thue-Morse morphism. We prove the analogue of
Fife's Theorem for faux-bonacci words, and characterize the lexicographically
least and greatest infinite faux-bonacci words.
