Supersaturated designs are an increasingly popular tool for screening factors in the presence of effect sparsity. The advantage of this class of designs over resolution III factorial designs or Plackett–Burman designs is that n, the number of runs, can be substantially smaller than the number of factors, m. A limitation associated with most supersaturated designs produced thus far is that the capability of these designs for estimating g active effects has not been discussed. In addition to exploring this capability, we develop a new class of model-robust supersaturated designs that, for a given n and m, maximizes the number g of active effects that can be estimated simultaneously. The capabilities of model-robust supersaturated designs for model discrimination are assessed using a model-discrimination criterion, the subspace angle. Finally, we introduce the class of partially supersaturated designs, intended for use when we require a specific subset of m1m1 core factors to be estimable, and the sparsity of effects principle applies to the remaining (m-m1m-m1) factors.