  A classical result of Cherbonnier and Colmez says that all \'etale $(\varphi,
\Gamma)$-modules are overconvergent. In this paper, we give another proof of
this fact when the base field $K$ is a finite extension of $\mathbb Q_p$.
Furthermore, we obtain an explicit ("uniform") lower bound for the
overconvergence radius, which was previously not known. The method is similar
to that in a previous joint paper with Tong Liu. Namely, we study Wach models
(when $K$ is unramified) in modulo $p^n$ Galois representations, and use them
to build an overconvergence basis.
