Inversion recovery sequences that vary the inversion time (t(i)) have been employed to determine T(1) and, more recently, quantitative magnetization transfer parameters. Specifically, in previous work, the inversion recovery pulse sequences varied t(i) only while maintaining a constant delay (t(d)) between repetitions. T(1) values were determined by fitting to a single exponential function, and quantitative magnetization transfer parameters were then determined by fitting to a biexponential function with an approximate solution. In the current study, new protocols are employed, which vary both t(i) and t(d) and fit the data with minimal approximations. Cramer-Rao lower bounds are calculated to search for acquisition schemes that will maximize the precision efficiencies of T(1) and quantitative magnetization transfer parameters. This approach is supported by Monte Carlo simulations. The optimal T(1) schemes are verified by measurements on MnCl(2) samples. The optimal quantitative magnetization transfer schemes are confirmed by measurements on a series of cross-linked bovine serum albumin phantoms of varying concentrations. The effects of varying the number of sampling data points are also explored, and a rapid acquisition scheme is demonstrated in vivo. These new optimized quantitative imaging methods provide an improved means for determining T(1) and magnetization transfer parameter values compared to previous inversion recovery based methods.