The basic features of this paper on implementation are the following: first, the social choice functions take their values in a space of lotteries; second, small fines may be levied on players. The solution concept is the iterative elimination of weakly dominated strategies. It is shown that any social choice function is implementable in iteratively weakly undominated strategies. The constructed mechanisms have a nice feature. For arbitrary normal form games, the order of removal of weakly dominated strategies matters. In the finite mechanism introduced by the authors, this does not hold.