In this paper, we study partially overlapping co-existence scenarios in cognitive radio environment. We consider an Orthogonal Frequency Division Multiplexing (OFDM) cognitive system coexisting with a narrow-band (NB) and an OFDM primary system, respectively. We focus on finding the minimum frequency separation between the coexisting systems to meet a certain target BER. Windowing and nulling are used as simple techniques to reduce the OFDM out-of-band radiations, and, hence decrease the separation. The effect of these techniques on the OFDM spectral efficiency and PAPR is also studied.