Keywords: Navier-Stokes equations, partial regularity, Hausdorff dimension, fractal dimension. Abstract: A classical result of Caffarelli, Kohn, and Nirenberg states that the one dimensional Hausdorff measure of singularities of a suitable weak solution of the Navier-Stokes system is zero. We present a short proof of the partial regularity result which allows the force to belong to a singular Morrey space. We also provide a new upper bound for the fractal dimension of the singular set.