  Let n_m be the smallest integer n such that ch(K_{m,n}) = m-1, where ch(G)
denotes the choice (list chromatic) number of the graph G. We prove that there
is an infinite sequence of integers S, such that if m is in S, then n_m <=
0.4643 ((m-2)^(m-2)). If m -> infinity, then n_m is asymptotically at most
0.474 ((m-2)^(m-2)).
