  It was shown by Bishop that if Thurston's $K = 2$ conjecture holds for some
planar domain, then Brennan's conjecture holds for the Riemann map of that
domain as well. In this paper we show numerically that the original
counterexample to Thurston's $K=2$ conjecture given by Epstein, Marden and
Markovi\'{c} is not a counterexample to Brennan's conjecture.
