In biochemical signaling, information is often encoded in oscillatory signals. However, the advantages of such a coding strategy over an amplitude-encoding scheme of constant signals remain unclear. Here we study the dynamics of a simple model gene promoter in response to oscillating and constant transcription factor signals. We find that in biologically relevant parameter regimes an oscillating input can produce a more constant protein level than a constant input. Our results suggest that oscillating signals may be used to minimize noise in gene regulation.