This paper explores the use of diophantinized fractional fits for the nonlinear constitutive representation of elastomeric media. These are caste in terms of either the principal stretches or the strain invariants. Both polynomial and rational forms are considered. To construct the requisite complete and physically admissible basis space, the diophantinized set of fractional powers is bound by the curvature properties of the experimental data set. This set is then employed in conjunction with a remezed least square scheme to obtain an optimal fit. To verify the scheme a sample application case is presented.