We address the problem of carrier frequency offset (CFO) synchronization in OFDM-based communications systems in the context of frequency-selective fading channels. A blind CFO estimator was recently developed, which exploits the virtual subcarriers (VSC) in a practical OFDM system. Here, we propose a semi-blind approach where a few (either zero or non-zero) pilots are inserted in the OFDM block. The semi-blind estimator (SBE) is shown to significantly outperform the blind estimator even with a few pilots provided they are equispaced, Further, the SME based on zero pilots consistently outperforms that based on non-zero pilots. Reliable estimation of an unknown frequency-selective channel requires that some (or all) of the pilots be non-zero, since zero pilots are useless for channel estimation. It is shown that if the total number of pilots is (much) larger that the channel order, zero pilots and non-zero pilots lead to almost the same CFO estimation performance. Therefore, in this case, non-zero pilots should be preferred to zero pilots.