This paper considers the problem of blind channel shortening in OFDM systems. Standard OFDM systems use guard interval (GI) in form of cyclic prefix (CP) and nulltones (NT) redundancy. In this paper, we are interested in exploiting simultaneously the CP and the NT to achieve blindly the channel shortening. We start by proving that the restoration of NT property leads to the desired channel shortening. However, the performance of the shortening based only on the NT is relatively poor. We propose to improve it by using the NT in conjunction with the CP redundancy. Hence, the GI-based shortening criterion is combined with the NT-based criterion via a scalar weighting coefficient. The latter is optimized to improve Symbol Error Rate (SER) performance of the receiver. Simulation results are provided to illustrate the performance of the combined criterion as compared to the GI-Based (MERRY algorithm) or NT-based criteria.