  A comprehensive theoretical approach to describe the electron-ion radiative
recombination in the presence of intense, short laser pulses, which accounts
for nondipole corrections is presented. It is based on the relativistic
Coulomb-Volkov solution describing an electron in a combined Coulomb potential
and a laser field, which is systematically expanded in powers of $1/c$. Thus,
it allows us to trace the origin of nondipole effects observed in the spectrum
of emitted radiation. Hence, as we demonstrate for high-frequency pulses
assisting the process, a significant extension of the cutoff and asymmetry in
angular distributions of the emitted radiation can be attributed to the
electron recoil off the laser pulse. In addition, we investigate a possibility
of enhancing the efficiency of the generated high-energy radiation by chirping
the pulse.
