We report here a systematic study of the energy gaps at the odd-integer quantum Hall states nu = 3 and 5 under tilted magnetic (B) fields in a high quality Si two-dimensional electron system. Out of the coincidence region, the valley splitting is independent of the in-plane fields. However, the nu = 3 valley gap differs by about a factor of 3 (Deltav approximately 0.4 vs 1.2 K) on different sides of the coincidence. More surprisingly, instead of reducing to zero, the energy gaps at nu = 3 and 5 rise rapidly when approaching the coincidence angles. We believe that such an anomaly is related to strong couplings of the nearly degenerate Landau levels.