We study the effects of drift motions and the advection by a Galactic wind on the propagation of cosmic rays in the Galaxy. We employ a simplified magnetic field model, based on (and similar to) the Jansson-Farrar model for the Galactic magnetic field. Diffusion is allowed to be anisotropic. The relevant equations are solved numerically, using a set of stochastic differential equations. Inclusion of drift and a Galactic wind significantly shortens the residence time of cosmic rays, even for moderate wind speeds