Accurate sinusoidal series models of biological time-series data may be obtained using a modeling algorithm known as fast orthogonal search (FOS). FOS does not require equally spaced data, and can resolve sinusoidal frequencies much more closely spaced than can a discrete Fourier transform. FOS has been less successful at obtaining accurate exponential series models. We here consider a modification of FOS in which iteration of the original procedure is used to further reduce the mean-squared error (m.s.e.) between model and data, approaching a minimum in the m.s.e. Iteration of the FOS procedure greatly improves the accuracy of estimated exponential series models. The application of iterative FOS (IFOS) to exponential and sinusoidal series models is described. Finally, the use of FOS and IFOS procedures for finding a single model from the results of multiple experiments is described.