  We generalize the well-known method of generating nondiffracting beams based
on axicons by allowing phase modulations with azimuthal dependencies. This
generalization includes the description of Bessel-like beams of zero order,
higher orders and superpositions thereof. We present the enormous benefit of
our approach for highly efficient and robust shaping of nondiffracting beams
with arbitrary transverse profiles. The concept's versatility is demonstrated
by discussing generation and propagation of various nondiffracting beams with
potential regarding laser materials processing.
