We discuss binary atomic collisions in a Bose gas tightly confined in one (
axial) direction and identify two regimes of scattering. In the quasi-two-d
imensional (quasi-2D) regime, where the confinement frequency omega (0) gre
atly exceeds the gas temperature T, the scattering rates exhibit 2D feature
s of the particle motion. At temperatures T similar to(h) over bar omega (0
) one has a confinement-dominated 3D regime, where the confinement can chan
ge the momentum dependence of the scattering amplitudes. We describe the co
llision-induced energy exchange between the axial and radial degrees of fre
edom and analyze recent experiments on thermalization and spin-relaxation r
ates in a tightly (axially) confined gas of Cs atoms.