In an OFDM system, antenna selection can be performed on a per-subcarrier basis, which can exploit the frequency selectivity of the channel. However, this may cause power imbalance across the antennas, which may lead to problems with the power amplifiers (PA). To avoid this problem, we devise a scheme that allocates the same number of subcarriers to all antennas, while still offering substantial diversity gains. This is achieved by using integer optimization and we show that this is solvable by linear relaxation, which results in a reduced complexity. The constrained antenna selection is analyzed and it is shown that choosing the cost function as BER offers better diversity gains than using SNR. Simulations with a nonlinear PA show that the integer optimization scheme performs better than unconstrained antenna selection and a previously published ad hoc method.