Recently, Bramble and Schatz have proposed a projection method for approximating the solution of Dirichlet's problem. Error estimates are derived by the authors using arguments based on certain interpolation theorems for linear operators on Hilbert spaces. It is shown here that simpler and shorter methods can be used to obtain these error estimates. 1. Introduction. The purpose of this note is to give a simplified proof of the results obtained by Bramble and Schatz in (1), where they proposed a method of least squares for obtaining approximations to solutions of Dirichlet's problem. To obtain error estimates in (1), Bramble and Schatz employed certain interpola- tion theorems for linear operators on Hilbert space, and, in particular, used these theorems in an iterative argument to get the results. Subsequently, an observation of Thomee (7) showed that the iterative argument mentioned above could be avoided with the use of appropriate trace theorems and a reformulation of the approximability assumptions on the subspaces used. This observation resulted in a slight simplification of the methods used in (1). Here, we present a new technique for obtaining the results of (1) which is much simpler and shorter than the prior ones. An entirely different approach is used which in essence involves a basic a priori estimate, and an argument based on duality. This new technique also yields a slight extention of the results of (1). In particular, the estimate (5.3) of Theorem 5.1 is new.