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In a market for a homogeneous good where firms are identical, compete in quantities and produce with constant returns, the percentage of welfare losses (PWL) is small with as few as five competitors for a class of demand functions which includes linear and isoelastic cases. We study markets with positive fixed costs and asymmetric firms. We provide exact formulae of PWL and robust constructions of markets were PWL is close to one in these two cases. We show that the market structure that maximizes PWL is either monopoly or dominant firm, depending on demand. Finally we prove that PWL is minimized when all firms are identical, a clear indication that the assumption of identical firms biases the estimation of PWL downwards.