Two algorithms for deconvolution, exploiting Tikhonov's regularisation idea, are briefly presented and tested to prove and demonstrate their effectiveness and usefulness for processing X-ray powder diffraction data. In one of them, suitable also for solving Fredholm's integral equations of the first kind in general form, matrix computations are involved, while in the other the fast Fourier transform is applied. The a-posteriori regularisation parameter choice criterion together with the data error estimation procedure is included in them. The results of computational test with simulated powder diffraction data illustrate the reliability and robustness of the algorithms.