In this paper, we consider searching for global minima of zero or small residual, nonlinear least-squares problems. We propose a selective search approach based on the concept of selective minimization recently introduced in Zhang et al[14]. To test the viability of the proposed approach, we construct a simple implementation using a Levenberg-Marquardt type method combined with a multi-start scheme, and compare it with several existing global optimization techniques. Numerical experiments were performed on zero residual nonlinear least-squares problem chosen from structural biology applications as well as from the literature. On the problems of larger sizes, the performance of the new approach compared favorably with the other tested methods, indicating that the new approach is promising for the intended class of problems.