  We analyze free conformal higher spin actions and the corresponding wave
operators in arbitrary even dimensions and backgrounds. We show that the wave
operators do not factorize in general, and identify the Weyl tensor and its
derivatives as the obstruction to factorization. We give a manifestly
factorized form for them on (A)dS backgrounds for arbitrary spin and on
Einstein backgrounds for spin 2. We are also able to fix the conformal wave
operator in d=4 for s=3 up to linear order in the Riemann tensor on generic
Bach-flat backgrounds.
