A multitude of applications contain signals that can be well described as being formed as a sum of sinusoidal com-ponents corrupted by noise, and, as a result, the literature contains a large variety of estimation algorithms tailored for this problem. Many of these estimators assume a complex-valued signal model, typically formed using the discrete-time Hilbert transform. For a large number of observations, or with frequencies being neither too high nor too low, this ap-proach works well, whereas it might well cause considerable problems otherwise. One way to handle these situations is to instead form the frequency estimation algorithm assuming a real-valued signal. In this paper, we show how the principle of angles between subspaces can be applied to this problem to alleviate some of the shortcomings of subspace-based fre-quency estimation using the MUSIC algorithm and demon-strate the resulting attractive properties via computer simula-tions.