A simple analytical approximation exists for the wave function of an u
nbound electron interacting both with a strong, circularly polarized l
aser field and an atomic Coulomb potential [1]. This wave function is
the Volkov state with a first-order Coulomb correction coming from som
e perturbative expansion of the potential in the Kramers-Henneberger r
eference frame [2-4]. The expansion is valid if the distance from the
center of the Coulomb force is smaller than the classical radius of mo
tion of a free electron in a plane-wave field. We generalize this appr
oach for any elliptic polarization. The total photoionization rate in
the strong-field approximation grows more for linear than for circular
polarization due to Coulomb correction.