  In the present work we constrain three different profiles of a
Lema\^itre-Tolman-Bondi model using supernovae type Ia and baryon acoustic
oscillation data. We improve common practice in the literature by carefully
calibrating the supernovae in the appropriate inhomogeneous background
dynamics. In addition, we address subtle issues in order to propagate the
primordial BAO scale to present epoch. The combined analysis of BAO+SNIa offers
a stringent test for these models. We use two distinct parameter estimation
approaches, namely, the $\chi^2$ and the complete likelihood functional. It has
been argued that these two approaches are not equivalent and indeed our
analysis shows a specific example of their departure.
