  New constraints on inhomogeneous Lema\^itre-Tolman-Bondi (LTB) models
alternative to Dark Energy are presented, focusing on adiabatic profiles with
space-independent Big Bang and baryon fraction. The Baryon Acoustic Oscillation
(BAO) scale at early times is computed in terms of the asymptotic value and
then projected to different redshifts by following the geodesics of the
background metric. Additionally, a model-independent method to constraint the
local expansion rate using a prior on supernovae luminosity is presented.
Cosmologies described by an adiabatic GBH matter profile with \Omega_{out}=1
and \Omega_{out}\leq 1 are investigated using a Markov Chain Monte Carlo
analysis including the latest BAO data from the WiggleZ collaboration and the
local expansion rate from the Hubble Space Telescope, together with Union-II
type Ia supernovae data and the position and height of the Cosmic Microwave
Background acoustic peaks. The addition of BAO data at higher redshifts
increases considerably their constraining power and represents a new drawback
for this type of models, yielding a value of the local density parameter
\Omega_{in}>0.2 which is 3\sigma apart from the value \Omega_{in}<0.15 found
using supernovae. The situation does not improve if the asymptotic flatness
assumption is dropped, and a Bayesian analysis shows that constrained GBH
models are ruled out at high confidence. We emphasize that these are purely
geometric probes, that only recently have become sufficiently constraining to
independently rule out the whole class of adiabatic LTB models.
