Several methods have recently been proposed for avoiding computational anomalies in the multichannel variational formalism of Kohn. The proposed methods themselves have characteristic difficulties, discussed in detail here, leading to ambiguous or discontinuous results. Two new methods are proposed. One, the optimized minimum-norm (OMN) method, is a development of the minimum-norm method of Harris and Michels. The other, the optimized anomaly-free (OAF) method, applies the idea of a preliminary unitary transformation of the open scattering channels to the anomaly-free method of Nesbet. Model calculations are reported that show both OMN and OAF methods to be superior to earlier methods. The OAF method has the additional advantage of avoiding anomalies that occur in the OMN method. © 1972 The American Physical Society.