  In this paper, we use the latest Higgs measurements from ATLAS and CMS to
constrain the parameter space of the model of Schmaltz, Stolarski and Thaler, a
Little Higgs model with two Higgs doublets, which we will refer to as the BLH
model. We account for all production and decay modes explored at ATLAS and CMS
in two scenarios: a general case, which assumes the $h_0$ state is light
($m_{h_0} \approx 125$ GeV) and the masses of the other neutral scalars ($H_0$
and $A_0$) are allowed to vary, and a case with a near-degeneracy between the
masses of the $h_0$ and $A_0$ and, for some choices of parameters, the $H_0$
states. The near-degeneracy scenario can result in an enhanced diphoton rate,
as measured by ATLAS, but is largely ruled out by a combination of the $h_0
\rightarrow \tau^+\tau^-$ and the heavy $H_0 \rightarrow W^+W^-$ measurements.
In the general case, we find large regions of parameter space that are in
better agreement with either the ATLAS or CMS results than is the SM. However,
a significantly enhanced diphoton rate is only possible through large
contributions to the $h_0 \gamma \gamma$ effective coupling from charged Higgs
bosons in a region of parameter space that borders on violation of
perturbativity in the scalar sector.
