We address the general problem of how best to attack and destroy a network by node removal, given limited or no prior information about the edges. We consider a family of strategies in which nodes are randomly chosen, but not removed. Instead, a random acquaintance (i.e., a first neighbour) of the chosen node is removed from the network. By assigning an informal cost to the information about the network structure, we show using cost-benefit analysis that acquaintance removal is the optimal strategy to destroy networks efficiently.