Contests are situations in which a set of agents compete for a valuable object, rent or award. The present paper analyzes difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. First, we show that the non-existence of pure-strategy equilibria and the monopolization results obtained in previous analysis of difference-form contests rest critically on the assumption of a linear cost of effort. Under exponential costs, we show that pure strategy equilibria exist in a large set of cases and that more than one group can expend positive effort in equilibrium. Second, we show that inequality of valuations of victory within groups hinders their chances of prevailing in the contest. If possible; members may find beneficial to engage in progressive redistribution within their group.