Consider the set of those binary words with no non-empty factors of the form xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this talk, we demonstrate the existence of upper and lower bounds on the number of such words of length n, where each of these bounds is asymptotically equivalent to a (different) function of the form Cn^{lg n+c}, where C, c are constants.