Superconducting tunnel junctions (STJs) offer the capability of photon counting with intrinsic energy resolving power. This resolving power is ultimately limited by the variance on the number of charge carriers generated in the photon absorption process (Fano limit) and the variance on the number of tunnelled charge carriers (tunnel limit). In addition, the performance can be degraded by electronic noise related to the read-out of the devices and by spatial non-uniformities in the response across the detector area. The present generation of our Ta-Al STJs is such that their spectroscopic performance in the UV/visible is limited by tunnel noise. This noise contribution is usually considered a device constant, (which may only vary marginally with bias conditions) and evaluated for infinite integration time. It can be shown, however, that the tunnel noise contribution is strongly time dependent and can be reduced by almost an order of magnitude for a properly chosen integration time. In this paper we present the experimental demonstration and numerical simulations of this time dependence on a series of Ta-Al STJs with different pulse decay times. The experimental results are in qualitative agreement with the simulations, but do not quite achieve the predicted performance. For the optimum configuration, an effective tunnel noise contribution of ~70% of the conventional tunnel limit is found.