A multipass absorption cell, based on an astigmatic variant of the off-axis resonator 1Herriott2 configuration, has been designed to obtain long path lengths in small volumes. Rotation of the mirror axes is used to obtain an effective adjustability in the two mirror radii. This allows one to compensate for errors in mirror radii that are encountered in manufacture, thereby generating the desired reentrant patterns with less-precise mirrors. A combination of mirror rotation and separation changes can be used to reach a variety of reentrant patterns and path lengths with a fixed set of astigmatic mirrors. The accessible patterns can be determined from trajectories, as a function of rotation and separation, through a general map of reentrant solutions. Desirable patterns for long-path spectroscopy can be chosen on the basis of path length, distance of the closest beam spot from the coupling hole, and tilt insensitivity. We describe the mathematics and analysis methods for the astigmatic cell with mirror rotation and then describe the design and test of prototype cells with this concept. Two cell designs are presented, a cell with 100-m path length in a volume of 3 L and a cell with 36-m path length in a volume of 0.3 L. Tests of low-volume absorption cells that use mirror rotation, designed for fast-flow atmospheric sampling, show the validity and the usefulness of the techniques that we have developed.