Mixed representations-polynomials in (v+1/2) at low v, near-dissociation expansions (NDEs) in (v(D)-v) at high v-are tested for their ability to fit a comprehensive and precise data set for the A state of I-2. The combined functions for the vibronic energy T-v and the rotational constant B-v are rendered smooth at the point of switchover through two approaches: the use of Lagrange's method of undetermined multipliers to incorporate exactly satisfied constraints for continuity in the functions and their first derivatives, and the use of a smooth switching function. As compared with a previously reported pure NDE analysis [Appadoo , J. Chem. Phys. 104, 903 (1996)], both approaches yield significantly reduced chi-square and a more realistic extrapolation of B-v from the highest analyzed level (v=35) to dissociation. The switching-function method has a number of advantages over the constraint method, and is thus recommended as the preferred approach for fitting to mixed representations. (C) 2003 American Institute of Physics.