This paper deals with the problem of structure determination for generalized orthonormal basis models used in system identification. The model structure is parametrized by a pre-specified set of poles. Given this structure and experimental data a model can be estimated using linear regression techniques. Since the variance of the estimated model increases with the number of estimated parameters, the objective is to find structures that are as compact/parsimonious as possible. A natural approach would be to estimate the poles, but this leads to nonlinear optimization with possible local minima. In this paper, a best basis algorithm is derived for the generalized orthonormal rational bases. Combined with linear regression and thresholding this leads to compact transfer function representations