We present the modal analysis and dispersion curves of some asymmetric annular optical-fiber waveguides. The proposed cross-sections can be conceived as having the shape of a distorted annular circular waveguide and leads to a tolerance study of deformation in an annular optical-fiber waveguide. We obtain mathematical expressions for the modes of the proposed waveguides using boundary matching techniques under some logical assumptions. We observe that the proposed distortions are able to tune the cutoff values of annular circular waveguide at desired levels.