Some theories of gravity, alternative to general relativity,
introduce a preferred rest frame for local gravitational physics.
At the post-Newtonian level, these preferred-frame effects in
lagrangian-based theories are described by two phenomenological
parameters $\alpha_1$ and $\alpha_2$, of which only the latter is
strongly constrained today. Following previous theoretical suggestions
of Nordtvedt, Damour and Vokrouhlick\'y we show that the
analysis of the lunar motion provides an improved bound
of the former parameter, notably $\alpha_1 = (-8 \pm 9)\times 10^{-5}$
realistic error [and $\alpha_1 = (-8\pm 4)\times 10^{-5}$ (90
\% C.L.)].