Gossiping has been considered intensively for butterries and \regular" butterries (which have no wrap-around connections). In the telephone communication model, for a butterry of order k, the best previous gossiping algorithms require 2 1 = 2 k and 3 k communication rounds, respectively. By new asymptotic methods we break through these bounds, proving new bounds of 2 1 = 4 k + o(k) and 2 1 = 2 ...
