  We consider the possibility to produce a bouncing universe in the framework
of scalar-tensor gravity when the scalar field has a nonconformal coupling to
the Ricci scalar. We prove that bouncing universes regular in the future with
essentially the same dynamics as for the conformal coupling case do exist when
the coupling deviates slightly from it. This is found numerically for more
substantial deviations as well. In some cases however new features are found
like the ability of the system to leave the effective phantom regime.
