Filter bank multicarrier (FBMC) systems that are based on offset quadrature amplitude modulation (OQAM), namely, FBMC-OQAM, have been criticized for their inefficiency in the use of spectral resources, because of the long ramp-up and ramp-down tails at the beginning and the end of each data packet, respectively. We propose a novel method for shortening these tails. By appending a set of virtual (i.e., none data carrying) symbols to the beginning and the end of each packet, and clever selection of these symbols, we show that the ramp-up and rampdown tails in FMBC-OQAM can be suppressed to an extent that they deem as negligible and thus may be ignored. This shortens the length of signal burst in each FBMC-OQAM packet, hence, improves on its bandwidth efficiency, viz., the same data is transmitted over a shorter period of time. We develop an optimization method that allows computation of virtual symbols, for each data packet. Simulation results show that, compared to existing methods, the proposed tail-shortening approach leads to a superior out-of-band (OOB) emission performance and a much lower error vector magnitude (EVM) for the demodulated symbols.