When adding laminar or 2-D margins to the clinical target volume (CTV), additional borders are required superiorly and inferiorly. Two common strategies for adding these margins, the cylindrical method (CYL) and the chamfer method (CHR), are discussed, and improved 2-D methods are presented. The improved cylindrical method (ICYL) extends the PTV superiorly and inferiorly, but the uppermost and lowermost PTV outlines are limited laterally to the extent of the CTV. If the required 3-D margin is M, the improved chamfer method (ICHR) constructs a transaxial margin of the square root of M2-d2 on a CT plane which is a distance d above the most superior CTV outline. For a theoretical tumor, CYL and CHR overestimate and underestimate the superior target margin by 8.1 cm3 and 9.6 cm3, respectively, whereas ICYL overestimates by only 2.2 cm3 and ICHR provides the desired margin. For eight esophageal tumors (specified margin 20 mm), CHR systematically underestimates the margin on the slice immediately inferior to the CTV by 7 mm (median, range 7-27 mm, p<0.01), while CYL overestimates the margin two slices inferior to the CTV by 20 mm in all cases. ICYL removes the overestimation of CYL, but retains an overestimation of 3 (-17-3) mm (p<0.01) on the first slice inferior to the CTV. ICHR performs most accurately, the margin width being equal to that of a true 3-D margin, except for occasional underestimations (0-33 mm, p<0.01). Similar results are demonstrated for eight prostatic tumors (specified margin 10 or 15 mm), but with the more irregular tumor shape causing all 2-D methods to underestimate the margin, most notably by 4.5 (0-21) mm (p<0.01) on the inferior CTV slice for a 15-mm margin. In general, both improved 2-D methods produce significantly more accurate margins than the conventional methods, the margin produced by the improved chamfer method most closely approximating a true 3-D margin.