  Recently there has been theoretical and experimental interest in
Bloch-Siegert shifts in an intense photon field. A perturbative treatment
becomes difficult in this multiphoton regime. We present a unitary transform
and rotated model, which allows us to get accurate results away from the level
anticrossings. A simple variational energy estimate leads to a new expression
for the dressed two-level system energy which is accurate, and useful over a
wide range of the dimensionless coupling constant.
