Intensity modulated radiation therapy (IMRT) treatment planning systems optimize fluence distributions by subdividing the fluence distribution into rectangular bixels. The algorithms typically optimize the fluence intensity directly, often leading to fluence distributions with sharp discontinuities. These discontinuities may yield difficulties in delivery of the fluence distribution, leading to inaccurate dose delivery. We have developed a method for decoupling the bixel intensities from the optimization parameters; either by introducing optimization control points from which the bixel intensities are interpolated or by parametrizing the fluence distribution using basis functions. In either case, the number of optimization search parameters is reduced from the direct bixel optimization method. To illustrate the concept, the technique is applied to two-dimensional idealized head and neck treatment plans. The interpolation algorithms investigated were nearest-neighbor, linear and cubic spline, and radial basis functions serve as the basis function test. The interpolation and basis function optimization techniques were compared against the direct bixel calculation. The number of optimization parameters were significantly reduced relative to the bixel optimization, and this was evident in the reduction of computation time of as much as 58% from the full bixel optimization. The dose distributions obtained using the reduced optimization parameter sets were very similar to the full bixel optimization when examined by dose distributions, statistics, and dose-volume histograms. To evaluate the sensitivity of the fluence calculations to spatial misalignment caused either by delivery errors or patient motion, the doses were recomputed with a 1 mm shift in each beam and compared to the unshifted distributions. Except for the nearest-neighbor algorithm, the reduced optimization parameter dose distributions were generally less sensitive to spatial shifts than the bixel optimization. These results indicate that significant reductions in optimization parameter sets can be accomplished with a negligible reduction in dose distribution quality. The decreased parameters can result in a reduced optimization time, or can be used to allow an improved and consequently more computation-intensive dose calculation for more accurate dose calculations during the optimization process. The basis functions may be generalized to model the accelerator motion for direct computation of the accelerator motion sequence, removing the need for developing an independent leaf sequence step.