New algorithms have been devised and implemented in the program SIR2007 for the deconvolution of Patterson maps via the use of implication transformations and of the minimum superposition function. The new algorithms concern several practical aspects, such as the use of weighted Patterson syntheses to simplify the recognition of useful pivot peaks, the definition of a ranking criterion for them, the introduction of an early figure of merit to discard useless pivots and the fast Fourier transform transposition of the RELAX algorithm, aiming to find the correct location when the current molecular model is translated with respect to the true position. The advantages of the new procedure have been assessed using a large set of test structures. The results have been analysed with respect to four parameters: the CPU time necessary for obtaining and recognizing the correct solution, the presence of heavy atoms, the complexity limit of the structures solvable ab initio, and the data resolution limit.