  We present a wide class of models which realise a bounce in a spatially flat
Friedmann universe in standard General Relativity. The key ingredient of the
theories we consider is a noncanonical, minimally coupled scalar field
belonging to the class of theories with Kinetic Gravity Braiding /
Galileon-like self-couplings. In these models, the universe smoothly evolves
from contraction to expansion, suffering neither from ghosts nor gradient
instabilities around the turning point. The end-point of the evolution can be a
standard radiation-domination era or an inflationary phase. We formulate
necessary restrictions for Lagrangians needed to obtain a healthy bounce and
illustrate our results with phase portraits for simple systems including the
recently proposed Galilean Genesis scenario.
