We present evidence that the performance of the traditional fully connected Hopfield model can be dramatically improved by carefully selecting an information-specific connectivity structure, while the synaptic weights of the selected connections are the same as in the Hopfield model. Starting from a completely disconnected network we let "genuine" Hebbian synaptic connections grow, one by one, until a desired degree of stability is achieved. Neural pathways are thus fixed not before, but durh~g the learning phase.