Nowadays the power of lasers with diffraction beam quality is on significant rise. But it is not easy to achieve ideal quality because of severe undesired distortions. Under different forms of distortion the beam shows different behavior. With any form of distortions there is the need to qualitatively characterize the beam quality. Three various qualitative criteria are most commonly used for this purpose, each of them describing the beam with one ratio: overlapping integral, Strehl ratio, and M2 parameter. All these criteria are well-known and frequently used in the literature, though the problem of their interrelation has never been discussed. In this paper we have analyzed the above mentioned criteria and have researched their interrelations in three most common types of beam quality degradation: thermal lens, electronic self-focusing, and spherical aberration. Approximate analytical expressions for all three criteria and three types of beam distortion are derived for Gaussian and super-Gaussian intensity shapes. The efficiency of characterizing those beams by various criteria is discussed.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.