Alternative methods which could be used to derive accurate atomic co-ordinates from the data provided by an X-ray investigation of a crystal structure are discussed. It is shown that the customary Fourier series method is closely related to the least-squares method applied to this problem by Hughes. On the basis of this result a way in which the Fourier method can be modified to give less weight to certain coefficients has been discovered. The effect of terminating the Fourier series or introducing an artificial temperature factor is also investigated from the point of view of the relation between the Fourier and least-squares solutions. It is concluded that no significant increase in accuracy could be obtained by abandoning the Fourier method.