The noise characteristics of a semiconductor punchthrough structure are examined for operation under low-field conditions, i.e. constant mobility, and for trap levels in the bandgap of the semiconductor. It is shown that the noise measure is decreased under the influence of trapping of injected carriers, for the small-signal injection approximation. With the increase of the concentration of traps, the noise measure decreases, but the frequency band, where it takes place, narrows and is displaced to a lower frequency.