Previous studies have described magnetization transfer (MT) Z-spectra in terms of a two-pool Bloch model, with six spin-system parameters KA, F, T1A, T1B, T2A, and T2B. By simulation, we show that a process including nonlinear constrained optimization can be used to accurately and uniquely estimate spin-system parameters from MT Z-spectra prepared by continuous wave (CW) RF irradiation. Experiments producing Z-spectra by pulsed RF irradiation give substantially different magnetization values, relative to MT acquisitions obtained by CW RF irradiation, at small offset frequencies, with a consequence that only T2B can be uniquely determined. However, several equalities and bounds involving four of the other parameters (KA, F, T1A, and T1B) are derived, which are applicable to pulsed data. These relationships allow calculation of "free pool" magnetization corresponding to complete saturation of the restricted pool, without requiring that this complete saturation be experimentally achieved. MT experimental data from pulsed RF irradiation on boiled egg albumin, obtained using a clinical whole-body MRI system, are analyzed using an optimization algorithm and the derived expressions.