In this paper, a commonly used third-order model of an induction motor with eight parameters is analyzed in order to classify the model parameters based on their degree of significance in the model behavior. Using the results of this classification, only the significant parameters of an induction motor need to be estimated from the measurements. The remainder of the parameters can be replaced by their typical values, which results in an optimization problem with a reduced dimension. The reduced parameter model needs less computation time and thus is better suited for real-time applications. The significance of this approach is greater when many induction motors or dynamic inductive loads in the system need to be identified. A nonlinear Least absolute shrinkage and selection operator (Lasso) term selection method is employed for this study. The Lasso method minimizes the sum of squared errors, with a constraint on the L1 norm of the parameter vector, which is used to push some parameters to zero. The main idea, when using this method for nonlinear models, involves incorporating the Lasso constraint in an iterative solution approach such as Gauss-Newton algorithm. This method reduces the variance of the parameter estimates, and simplifies the interpretation of the model. To evaluate the performance of the proposed algorithm, the parameters of an induction motor are estimated. Estimation is performed both for simulated and experimental data. The results of the proposed approach are compared to those of a method based on sensitivity analysis.