Much of our commerce and travel depends on the efficient operation of large scale networks. Some of those, such as electric power grids, transportation systems, communication networks, and others, must maintain their efficiency even after several failures, or malicious attacks. We outline a procedure that modifies any given network to enhance its robustness, defined as the size of its largest connected component after a succession of attacks, whilst keeping a high efficiency, described in terms of the shortest paths among nodes. We also show that this generated set of networks is very similar to networks optimized for robustness in several aspects such as high assortativity and the presence of an onion-like structure.