  We propose a $\mu-\tau$ reflection symmetric Littlest Seesaw ($\mu\tau$-LSS)
model. In this model the two mass parameters of the LSS model are fixed to be
in a special ratio by symmetry, so that the resulting neutrino mass matrix in
the flavour basis (after the seesaw mechanism has been applied) satisfies
$\mu-\tau$ reflection symmetry and has only one free adjustable parameter,
namely an overall free mass scale. However the physical low energy predictions
of the neutrino masses and lepton mixing angles and CP phases are subject to
renormalisation group (RG) corrections, which introduces further parameters.
Although the high energy model is rather complicated, involving $(S_4\times
U(1))^2$ and supersymmetry, with many flavons and driving fields, the low
energy neutrino mass matrix has ultimate simplicity.
