According to the Lagrange--Helmholtz law, no optical system can ever increase the brightness (and therefore the effective temperature) of a light beam. This limitation is frequently interpreted as a consequence of the second law of thermodynamics. Actually, thermodynamics imposes no limitations of practical importance on the possibilities of increasing the brightness of light beams: the decrease of the entropy of the light beam associated with the increase of its brightness can be compensated by a loss of a negligible fraction of the energy of the beam. The general discussions are illustrated by a number of specific examples.