We propose two original methods of denoising of the uterine electrohysterography (EHG) signal by wavelets. This external electrophysiological signal is corrupted by electronic, electromagnetic noises and by the remaining electrocardiogram of the mother. The interfering signals have overlapping spectra. Therefore, a classical filtering is unusable. Wavelets should be a very well-suited denoising tool. The first proposed method uses the algorithm "à trou" with nonsymmetrical filters. The computation is rapid and the results are satisfying compared to the classical denoising techniques. The second algorithm is an improvement of the first method. It uses orthogonal wavelets and the result of the thresholding corresponds to the average of all circulant shifts denoised by a decimated wavelet transform. Results are compared to traditional denoising algorithms by wavelet (orthogonal, maximally decimated). The proposed algorithms are more efficient on simulated signals as well as on uterine EHG.