Submitted on 12 Feb 2008 (v1), last revised 28 Feb 2008 (this version, v2).-- Added references.-- 27 pages, 8 figures.-- A general Fortran program for comparing LTB models with cosmological observations, that has been used to make the parameter scan in this paper is made public, and can be downloaded at: http://www.phys.au.dk/~haugboel/software.shtml.-- Match version submitted to JCAP.The possibility that we live in a special place in the universe, close to the center 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 has 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-deSitter model.We thank the Danish Centre of Scientific Computing (DCSC) for granting the computer resources used. JGB would like to thank the Kavli Institute for Theoretical Physics for hospitality during the last stages of the work, supported in part by the National Science Foundation under Grant No. PHY05- 51164. We also acknowledge financial support from the Spanish Research Ministry (M.E.C.), under the contract FPA2006-05807.Peer reviewed