We prove local H"older continuity results for $$extract_itex$$\omega$$/extract_itex$$-minimizers of a class of functionals with non-standard growth, characterized by the fact of having a double type of degeneracy. As a side benefit of the proof, we also consider a class of functionals with Orlicz-growth and prove regularity for $$extract_itex$$\omega$$/extract_itex$$-minimizers.