The requirements and trade-offs between accuracy and speed for radiotherapy dose computations have been discussed for decades. Inverse planning used for intensity-modulated radiotherapy (IMRT) optimization imposes additional demands on dose calculation since it is an iterative process in which dose calculations might be repeated many (10's to 1000's) of times. This work discusses the accuracy and speed issues as related to IMRT dose calculations. A hybrid dose calculation method which accelerates the optimization process is proposed and applied in which a fast-pencil beam (PB) model is used for initial optimization iterations, followed by superposition/convolution (SC) calculations. Optimization dose results are compared for pure PB optimization, pure SC optimization, and PB optimization followed by SC optimization. Plans were evaluated in terms of isodose coverage, dose-volume histograms, and total dose calculation time for five head and neck cases with diverse locations, sizes, and shapes for tumors and critical structures. Patient plans were designed for nine equispaced beams. For one patient, an additional five-beam configuration was tested. We found that gross features of intensity distributions resulting from all schemes were similar, however there were differences in the fine detail. Differences were small between composite dose distributions optimized with PB and SC methods, yet differences in individual beam dose distributions were quite significant. When the SC method was used to compute dose following optimization with PB method, dose differences were reduced significantly both for composite plans and for individual beams. Substantial overall timesavings were observed, allowing IMRT dose planning to become a more interactive activity.