Optical-fiber refractive-index profiles perturbed near the fiber axis are characterized by using a new method based on moments of the profile function rather than its precise shape. The method is applied to waveguide dispersion for the fundamental mode, and results of widespread applicability are obtained. For step-index fibers perturbed out to 0.4 of the fiber-core radius, the dispersion behavior is described in terms of two parameters encompassing all possible perturbations. It is argued that it is more appropriate to study waveguide dispersion at the point at which the effective waveguide parameter V¯=3 rather than to concentrate on the point of zero dispersion.