  The formation of stellar mass black holes is still very uncertain. Two main
uncertainties are the amount of mass ejected in the supernova event (if any)
and the magnitude of the natal kick the black hole receives at birth (if any).
Repetto et al. (2012), studying the position of Galactic X-ray binaries
containing black holes, found evidence for black holes receiving high natal
kicks at birth. In this Paper we extend that study, taking into account the
previous binary evolution of the sources as well. The seven short-period
black-hole X-ray binaries that we use, are compact binaries consisting of a
low-mass star orbiting a black hole in a period less than $1$ day. We trace
their binary evolution backwards in time, from the current observed state of
mass-transfer, to the moment the black hole was formed, and we add the extra
information on the kinematics of the binaries. We find that several systems
could be explained by no natal kick, just mass ejection, while for two systems
(and possibly more) a high kick is required. So unless the latter have an
alternative formation, such as within a globular cluster, we conclude that at
least some black holes get high kicks. This challenges the standard picture
that black hole kicks would be scaled down from neutron star kicks.
Furthermore, we find that five systems could have formed with a non-zero natal
kick but zero mass ejected (i.e. no supernova) at formation, as predicted by
neutrino-driven natal kicks.
