Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reduced-order optimization methods that reduce the size of the control vector by projecting it onto a limited number of basis functions were suggested. In this paper, we show that such order reduction can indeed speed up the initial convergence rate of an assimilation effort in the eastern subtropical North Atlantic using in situ and satellite data as constraints. However, an improved performance of the optimization was only obtained with a hybrid approach where the optimization is started in a reduced subspace but is continued subsequently using the full control space. In such an experiment about 50% of the computational cost can be saved as compared to the optimization in the full control space. Although several order-reduction approaches seem feasible, the best result was obtained by projecting the control vector onto Empirical Orthogonal Functions (EOFs) computed from a set of adjusted control vectors estimated previously from an optimization using the same model configuration.