  We analyze the scalar potential of the Simplest Little Higgs (SLH) model in
an approach consistent with the spirit of continuum effective field theory
(CEFT). By requiring correct electroweak symmetry breaking (EWSB) with the
$125\,\text{GeV}$ Higgs boson, we are able to derive a relation between the
pseudo-axion mass $m_\eta$ and the heavy top mass $m_T$, which serves as a
crucial test of the SLH mechanism. By requiring $m_\eta^2>0$ an upper bound on
$m_T$ can be obtained for any fixed SLH global symmetry breaking scale $f$. We
also point out that an absolute upper bound on $f$ can be obtained by imposing
partial wave unitarity constraint, which in turn leads to absolute upper bounds
of $m_T\lesssim 19\,\text{TeV}, m_\eta\lesssim 1.5\,\text{TeV}$ and
$m_{Z'}\lesssim 48\,\text{TeV}$. We present the allowed region in the
three-dimensional parameter space characterized by $f,t_\beta,m_T$, taking into
account the requirement of valid EWSB and the constraint from perturbative
unitarity. We also propose a strategy of analyzing the fine-tuning problem
consistent with the spirit of CEFT and apply it to the SLH. We suggest that the
scalar potential and fine-tuning analysis strategies adopted here should also
be applicable to a wide class of Little Higgs and Twin Higgs models, which may
reveal interesting relations as crucial tests of the related EWSB mechanism and
provide a new perspective on assessing their degree of fine-tuning.
