In so-called compact two-mirror focusing and afocal systems the secondary mirror is situated at the paraxial focus of the spherical primary mirror. The peculiar conelike shape of the secondary is chosen to eliminate the spherical aberration. Thus the systems are stigmatic, but they have a great offence against the sine condition (OSC), creating uneven distribution of energy on the surface of the outgoing wavefront. There is a substantial concentration of energy toward the optical axis, similar to apodization of the pupil. Calculations of the point spread function (PSF) show that in such systems, the Airy disk is slightly enlarged (at most 20%) and the second maximum (the first bright ring) can be completely suppressed. The most effective suppression of the second and higher maxima in the diffraction pattern is obtained with an imposed central obscuration ratio of 0.5 and a primary mirror focal ratio of 2. Compact two-mirror afocal and focusing systems have intrinsic apodization, enabling modification of the diffraction pattern without the use of a variable transmission filter or coating at the pupil. © 2002 Society of Photo-Optical Instrumentation Engineers.