Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. Breaking with the traditional approach to these so called small worlds that relies mainly on graph parameters directly related to connectivity, we investigate the capacity of these networks from the perspective of network information flow. Our contribution includes upper and lower bounds for the capacity of standard and navigable small-world models based on added shortcuts, and the somewhat surprising result, that, with high probability, random rewiring does not alter the capacity of a small-world network.