We present an efficient method for estimating variables and parameters of a given system of ordinary differential equations by adapting the model output to an observed time series from the (physical) process described by the model. The proposed method is based on (unconstrained) nonlinear optimization exploiting the particular structure of the relevant cost function. To illustrate the features and performance of the method, simulations are presented using chaotic time series generated by the Colpitts oscillator, the three-dimensional Hindmarsh-Rose neuron model, and a nine-dimensional extended Rössler system.