In this article, I present a method for the nonparametric (model-free) estimation of intensity profiles underlying gamma-ray bursts. The algorithm, called TIPSH, is based on applying specially calibrated thresholds to the Haar wavelet coefficients of binned counts gathered from such bursts. Because wavelets are well-localized with respect to both time and scale, they are an ideal tool for working with the often sharp, abrupt nature of gamma-ray burst signals. When applied to an idealized signal in a small simulation study and a selection of actual gamma-ray bursts, the TIPSH algorithm was found to be well capable of simultaneously estimating the smooth, uniform background and the pulse-like structure of gamma-ray burst signals.