The possibility that we live in a special place in the universe, close to the centre of a large void, seems an appealing alternative to the prevailing interpretation of the acceleration of the universe in terms of a LCDM model with a dominant dark energy component. In this paper we confront the asymptotically flat Lemaitre-Tolman-Bondi (LTB) models with a series of observations, from Type Ia Supernovae to Cosmic Microwave Background and Baryon Acoustic Oscillations data. We propose two concrete LTB models describing a local void in which the only arbitrary functions are the radial dependence of the matter density Omega_M and the Hubble expansion rate H. We find that all observations can be accommodated within 1 sigma, for our models with 4 or 5 independent parameters. The best fit models have a chi^2 very close to that of the LCDM model. We perform a simple Bayesian analysis and show that one cannot exclude the hypothesis that we live within a large local void of an otherwise Einstein-de Sitter model.