Orthogonal frequency division multiplexing (OFDM) is a popular modulation scheme used in a variety of applications. One significant problem associated with OFDM is the possibility of large side-lobes in its spectrum. In this paper, we consider the so-called N-continuous method for reducing the side-lobes. We first consider one implementation approach, whereby certain sub-carriers are reserved for the purpose of adjusting the spectrum of an OFDM symbol. We find that significant side-lobe reduction is possible, although at the cost of injecting very large power in the reserved sub-carriers that results in unacceptable spectrum overshoot. In order to achieve reasonable power levels, at least 20% of all sub-carriers must be reserved for weighting. As a solution to the problem of spectrum overshoot, we propose an alternative approach whereby the power of the reserved sub-carriers is constrained. Numerical results show that reasonable power levels are achieved at the cost of significant performance loss in the N-continuous OFDM technique for side-lobe reduction. We thus find that the performance cost of eliminating the spectrum overshoot reduces the side-lobes reduction to less than 5 dB in cases of interest.