It is concluded that faint members found in the vicinities of compact groups (CGs) are gravitationally bound with corresponding groups. All members of CGs, faint and bright, move preferentially in the direction of the elongation of the group. We suppose that the number of faint members may be much larger than previously assumed. These two circumstances should apparently change the conclusion about the short lifetime of CGs. Consequently, many puzzles related to CGs, such as their very existence, the absence of strong radio and infrared sources, and the absence of strong signs of interaction and merging will probably vanish.