In this work we study the percolation phase transition of a family of scale-free networks previously introduced to explain the emergence of fractality and self-similarity in complex networks. This model introduces a parameter, e, that allows for tuning the level of fractality in the network. When e = 0 the network is a pure fractal, when e = 1 it is a pure small-world network. We examine link percolation for several intermediate values of e (0 <=, e <= 1), and find that the transition follows a continuous function of e that converges to exactly 0 when the network exhibits the small-world property. (C) 2009 Elsevier Ltd. All rights reserved.