NL2SOL is a modular program for solving nonlinear least-squares problems that incorporates novel features. It maintains a secant approximation of the second-order part of the least-squares Hessian and adaptively decides when to use it. The step choice algorithm minimizes a quadratic model of the sum of squares function constrained to an elliptical trust region. This approach is based on ideas from Moré and includes a module to assess the quality of the computed step. The algorithm also includes a sizing strategy similar to Oren-Luenburger scaling. The paper discusses the algorithm's development, its evolution, and current implementation. Key topics include unconstrained optimization, nonlinear least squares, and quasi-Newton methods. The algorithm is described in detail, including its convergence criteria, covariance matrix computation, and test results. NL2SOL is compared with other algorithms, such as SUMSOL, and shown to perform well in terms of function and gradient evaluations. The code is larger than a simple Levenberg-Marquardt implementation due to its adaptive modeling and reverse communication features. Timing experiments show that reverse communication and adaptive modeling add only a small overhead to execution time.NL2SOL is a modular program for solving nonlinear least-squares problems that incorporates novel features. It maintains a secant approximation of the second-order part of the least-squares Hessian and adaptively decides when to use it. The step choice algorithm minimizes a quadratic model of the sum of squares function constrained to an elliptical trust region. This approach is based on ideas from Moré and includes a module to assess the quality of the computed step. The algorithm also includes a sizing strategy similar to Oren-Luenburger scaling. The paper discusses the algorithm's development, its evolution, and current implementation. Key topics include unconstrained optimization, nonlinear least squares, and quasi-Newton methods. The algorithm is described in detail, including its convergence criteria, covariance matrix computation, and test results. NL2SOL is compared with other algorithms, such as SUMSOL, and shown to perform well in terms of function and gradient evaluations. The code is larger than a simple Levenberg-Marquardt implementation due to its adaptive modeling and reverse communication features. Timing experiments show that reverse communication and adaptive modeling add only a small overhead to execution time.