Intensity-modulated radiation therapy (IMRT) requires the determination of the appropriate multileaf collimator settings to deliver an intensity map. The purpose of this work was to attempt to reduce the number of segments required for IMRT delivery and the number of monitor units required to deliver an intensity map. An intensity map may be written as a matrix. Leaf sequencing was formulated as a problem of decomposing the matrix into a series of sub-matrices. Sets of random intensity matrices were created and the segmentations produced by applying different algorithms were compared. The number of segments, important if verification and record (VR) overhead is significant, and beam on times were examined. It is shown that reducing the value of the matrix entries by the maximum amount at each stage results in the smallest number of steps. Reducing the 2-norm (sum of the squares) of the matrix entries by the maximum amount at each step results in the smallest beam on time. Three new algorithms are introduced, two of which produce results that are superior to those generated by the algorithms of other researchers. The resulting methods can be expanded upon to include tongue and groove effects and leaf inter-digitization. With square random matrices of the order 15, the reduction in beam time and segmentation is up to 30-40%. Compared to previous algorithms, those presented here have demonstrated a reduction in the beam on time required to deliver an intensity map by 30-40%. Similarly, the number of segments needed to deliver an intensity map is also reduced.