  We present an improved version of commutator methods for unitary operators
under a weak regularity condition. Once applied to a unitary operator, the
method typically leads to the absence of singularly continuous spectrum and to
the local finiteness of point spectrum. Large families of locally smooth
operators are also exhibited. Half of the paper is dedicated to applications,
and a special emphasize is put on the study of cocycles over irrational
rotations. It is apparently the first time that commutator methods are applied
in the context of rotation algebras, for the study of their generators.
