Some new procedures for minimum residual factor analysis are presented. First a successive method developed by Comrey is modified in order to guarantee convergence and to provide a way to handle Heywood cases. Next, this modified Comrey procedure is extended to a simultaneous procedure which is computationally simpler and faster than the Minres method developed by Harman and Jones. This latter method, however, satisfies a stronger necessary condition for the minimum of the sum of squared off-diagonal residuals. Some empirical results are presented. These are in accordance with the theoretical considerations; that is, the Harman and Jones procedure tends to be slower, but attains in general a lower value for the sum of squared off-diagonal residuals.