Multi-element antennas offer the possibility of increasing the spatial reuse of wireless spectrum by “nulling” out interfering signals. However, the interference suppression performance is highly sensitive to small errors in the gains applied to the antenna elements. In this paper, we examine in detail the effect of one specific source of error that arises from quantizing array weights. We show that a simple approach based on scalar quantization that ignores the correlation of the quantization errors fails to fully utilize the interference suppression capability of the array: the residual interference level does not decrease with the number of antennas. Unfortunately, the optimum approach to computing the weights involves vector quantization over a space that grows exponentially with the number of antennas and number of quantization bits, and is therefore computationally intractable. We propose instead a simple suboptimal method that greedily optimizes the SIR, coefficient-by-coefficient. Simulations show that this greedy approach provides substantial SIR gains over the naive approach, with SIR growing polynomially in the number of antennas. We derive analytical bounds that indicate that even larger SIR gains (exponential in the number of antennas) are potentially achievable, so that finding tractable algorithms that improve upon our suboptimal approach is an important open problem.