A fundamental issue in NMR spectroscopy is the estimation of parameters such as the Larmor frequencies of nuclei, J coupling constants, and relaxation rates. The Cramer-Rao lower bound provides a method to assess the best achievable accuracy of parameter estimates resulting from an unbiased estimation procedure. We show how the Cramer-Rao lower bound can be calculated for data obtained from multidimensional NMR experiments. The Cramer-Rao lower bound is compared to the variance of parameter estimates for simulated data using a least-squares estimation procedure. It is also shown how our results on the Cramer-Rao lower bound can be used to analyze whether an experimental design can be improved to provide experimental data which can result in parameter estimates with higher accuracy. The concept of nonuniform averaging in the indirect dimension is introduced and studied in connection with nonuniform sampling of the data.