  We study the predictions for the matter redshift-space power spectrum and
correlation function of a Lagrangian-space Gaussian ansatz introduced in a
previous work. This model is a natural extension of the Zeldovich
approximation, where the displacement and velocity power spectra are determined
by the equations of motion, instead of being set equal to the linear power
spectrum. It does not contain any free parameter. As for the real-space
statistics, we find that this Lagrangian-space approach is much more efficient
for the correlation functions than for the power spectra. The damping of the
BAO oscillations is well recovered but there is a large smooth drift from the
simulations in the power spectra. The multipoles of the correlation functions
are well recovered on BAO scales, with an accuracy of $2\%$ for $\xi^s_0$ down
to $10 h^{-1}$ Mpc, and of $3\%$ for $\xi^s_2$ down to $26 h^{-1}$ Mpc, at $z
\geq 0.35$.
