In the past few years, there has been an increasing interest among the Brain-Computer Interface research community in classification algorithms that respect the intrinsic geometry of covariance matrices. These methods are based on concepts of Riemannian geometry and, despite demonstrating good performances on several occasions, do not scale well when the number of electrodes increases. In this paper, we evaluate two methods for reducing the dimension of the covariance matrices in a geometry-aware fashion. Our results on three different datasets show that it is possible to considerably reduce the dimension of covariance matrices without losing classification power.