Frequency-resolved optical gating (FROG) is a technique for measuring ultrashort laser pulses that involves producing a spectrogram of the pulse and then retrieving the intensity and phase of the electric field using a phase-retrieval algorithm. Since noise on experimental FROG traces reduces the performance of the retrieval algorithm, removing the noise is crucial. In previous work we have shown that subtracting the mean of the noise, optimized lowpass filtering, and suppression of the corners of the trace provides an efficient tool for denoising FROG traces. The recent development of wavelet noise-reduction techniques for signal and image processing now provides a new method for attacking this problem. We apply a two- dimensional discrete wavelet transform to the noisy FROG trace, threshold the wavelet coefficients, and perform the inverse wavelet transform to regain the trace. In combination with other noise-filtering methods, this efficiently removes noise from the trace and improves the algorithm's ability to retrieve the intensity and phase of the pulse accurately, especially in fairly low-noise situations, where extremely high accuracy is desired. In addition to wavelet- coefficient thresholding, we also investigate the possibility of using a geometrical scheme for filtering the wavelet coefficients, thus combining data compression and noise reduction.