We present a method to reduce noise in helioseismic power spectra using a non-orthogonal wavelet transform based on quadratic spline functions. The quality of our method is tested by applying it to artificially generated time-series approximating solar p-modes. The mode frequencies and line widths obtained from least-squares fits to the smoothed spectra are compared with the corresponding parameters deduced from maximum likelihood fits to the original spectra. The results from both approaches are very similar and suggest that there is no major bias in either of these rather independent approaches. As a practical example we denoise parts of the power spectrum obtained from the two first years of operation of the GOLF instrument onboard SOHO.