Gamma-Mn alloys show a host of antiferromagnetic phase transitions. Recently it has been suggested that the alloy disorder causes these phase transitions by locally trapping 'islands' of non-collinear spin density. Practical experimental studies of this possibility have previously been reported in the literature, employing magnetic diffuse scattering. Although basic agreement was obtained for some alloys, gamma-Mn(1-x)Cu(x) exhibited spectacular effects which have so far proven rather difficult to explain: so-called 'giant staggered moments'. We present a model which successfully predicts the magnetic diffuse scattering and explains the special behaviour observed in gamma-Mn(1-x)Cu(x) as arising from the local clustering of copper impurities.