Connectionist attractor networks have played a central role in many cognitive models involving associative memory and soft constraint satisfaction. While early attractor networks used step activation functions, permitting the construction of attractors for only binary (or bipolar) patterns, much recent work has focused on networks with continuous sigmoidal activation functions. The incorporation of sigmoidal processing elements allows for the use of expressive real vector representations in attractor networks. The empirical studies reported here, however, reveal that the learning performance of sigmoidal attractor networks is best when such general real vectors are avoided --- when training patterns are explicitly placed in the extreme corners of the network's activation space. Using binary (or bipolar) patterns produces benefits in the number of attractors learnable by a network, in the accuracy of the learned attractors, and in the amount of training required. These ben...