We discuss a counterintuitive phenomenon of classical general relativity, in which a significant fraction of the radiation emitted by a collapsing object and detected by a distant observer may be blueshifted rather than redshifted. The key-point is that when the radiation propagates inside the collapsing body it is blueshifted, and this time interval may be sufficiently long for the effect to be larger than the later redshift due to the propagation in the vacuum exterior, from the surface of the body to the distant observer. Unfortunately, the phenomenon can unlikely have direct observational implications, but it is interesting by itself as a pure relativistic effect.

6 pages, 3 figures. v2: refereed version