This paper presents computational results for some alternative methods of analysing multivariate data with missing values. We recommend an algorithm due to Orchard and Woodbury (1972), which gives an estimator that is maximum likelihood when the data come from a multivariate normal population. We include a derivation of the estimator that does not assume a multivariate normal population, as an iterated form of Buck's (1960) method. We derive an approximate method of assigning standard errors to regression coefficients estimated from incomplete observations, and quote supporting evidence from simulation studies. A brief account is given of the application of these methods to some school examinations data.