We study generalizations of the Hopfield model for associative memory which contain interactions of R spins with one another and allow for different weights for input patterns. Using probabilistic considerations we show that stability criteria lead to capacities which increase like powers of N**R** minus **1. Investigating numerically the basins of attraction we find behavior which agrees with theoretical expectations. We introduce the more stringent definition of 'converage-capacity' by requiring the whole phase-space to be covered by the basins of attraction of the input patterns. Even under these conditions we find large numbers of patterns which can be used to design an output spectrum by varying the input weights.