NL2SOL is a modular program designed to solve nonlinear least-squares problems with several novel features. It maintains a secant approximation to the second-order part of the least-squares Hessian and adaptively decides when to use this approximation. The approximation is "sized" before updating, similar to Oren-Luenberger scaling. The step choice algorithm minimizes a local quadratic model of the sum of squares function constrained to an elliptical trust region centered at the current approximate minimizer. This is achieved using ideas from Moré, along with a special module for assessing the quality of the step. The paper discusses these ideas and the evolution and current implementation of NL2SOL. Key features include an augmented Gauss-Newton model, sizing of the Hessian augmentation, adaptive quadratic modeling, and various convergence criteria. Test results show that NL2SOL performs well compared to other algorithms, particularly in terms of function and gradient evaluations. The code size and timing are also discussed, highlighting the benefits of reverse communication and adaptive modeling.NL2SOL is a modular program designed to solve nonlinear least-squares problems with several novel features. It maintains a secant approximation to the second-order part of the least-squares Hessian and adaptively decides when to use this approximation. The approximation is "sized" before updating, similar to Oren-Luenberger scaling. The step choice algorithm minimizes a local quadratic model of the sum of squares function constrained to an elliptical trust region centered at the current approximate minimizer. This is achieved using ideas from Moré, along with a special module for assessing the quality of the step. The paper discusses these ideas and the evolution and current implementation of NL2SOL. Key features include an augmented Gauss-Newton model, sizing of the Hessian augmentation, adaptive quadratic modeling, and various convergence criteria. Test results show that NL2SOL performs well compared to other algorithms, particularly in terms of function and gradient evaluations. The code size and timing are also discussed, highlighting the benefits of reverse communication and adaptive modeling.