  Based on an analysis of a specific electron trajectory in counter-propagating
beams, Bell & Kirk (PRL 101, 200403 (2008)) recently suggested that laboratory
lasers may shortly be able to produce significant numbers of electron-positron
pairs. We confirm their results using an improved treatment of nonlinear
Compton scattering in the laser beams. Implementing an algorithm that
integrates classical electron trajectories, we then examine a wide range of
laser pulse shapes and polarizations. We find that counter-propagating,
linearly polarized beams, with either aligned or crossed orientation, are
likely to initiate a pair avalanche at intensities of approximately 10^{24}
Watts/sq cm per beam. The same result is found by modelling one of the beams as
a wave reflected at the surface of an overdense solid.
