Several common optical-constant models do not satisfy a necessary requirement they are not analytic (in the sense of holomorphic). This includes models defined with a piecewise function like Tauc-Lorentz, Cody-Lorentz (CL), and Campi-Coriasso, and models with poles in the upper complex half plane. The consequence of this is an intrinsic inaccuracy. Sellmeier model, even though analytic, involves mostly unnatural divergences. A procedure is presented that turns non-analytic optical models into analytic by using the original model as a weight function in an integral over the spectrum using a small broadening parameter. Specific equations are obtained for the weight function being either the dispersion or the absorption part of the optical constants of the non-analytic model. The resulting optical-constant model can be differentiated to any order. The procedure is applied to turn analytic CL model and to remove the divergences from Sellmeier model. The analyticized CL model is applied to fit boron film optical constants.