  This work concerns the boundary integrability of the spin-s
${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb model. A systematic computation method is
used to constructed the solutions of the boundary Yang-Baxter equations. For
$s$ half-integer, a general $2s(s+1)+3/2$ free parameter solution is presented.
It turns that for $s$ integer, the general solution has $2s(s+1)+1$ free
parameters. Moreover, some particular solutions are discussed.
