  Consider the one-dimensional discrete Schr\"odinger operator $H_{\theta}$:
$$(H_{\theta} q)_n=-(q_{n+1}+q_{n-1})+ V(\theta+n\omega) q_n \ , \quad n\in Z \
,$$ with $\omega\in R^d$ Diophantine, and $V$ a real-analytic function on $
T^d=( R/2\pi Z)^d$. For $V$ sufficiently small, we prove the dispersive
estimate: {for every $\phi\in\ell^1( Z)$,} $$
  \| e^{-{\rm i}tH_{\theta}}\phi \|_{\ell^\infty} \leq K_0 \frac{
  |\ln\varepsilon_0|^{a(\ln\ln(2+\langle t\rangle))^2 d}} {\langle
  t\rangle^{\frac13}} \|\phi\|_{\ell^1} \ , \quad \langle t
\rangle:=\sqrt{1+t^2} \ ,$$ {with $a$ and $K_0$ two absolute constants} and
$\varepsilon_0$ an analytic norm of $V$. The estimate holds for every
$\theta\in T^d$.
