Under certain conditions, Burg maximum entropy spectra of sampled sine waves, in the presence of additive Gaussian white noise, show either spontaneous line splitting (at low noise levels) or appreciable frequency shifting (at moderate noise levels). This difficulty arises because an unnecessary constraint is imposed during the minimization of the prediction error power. When the constraint is relaxed and a lighter one imposed, the error power decreases and the problem is solved. The nature of the constraint is discussed, and the mathematical details of the new method are presented. The new method is verified by using a few simple test cases in which spontaneous line splitting is healed or frequency shifting is reduced drastically (Fougere, 1975).