Filter bank multicarrier (FBMC) systems 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 ramp-down tails in the FBMC-OQAM can be suppressed to the extent that they are deemed negligible and thus may be ignored. This shortens the length of signal burst in each FBMC-OQAM packet and improves its spectral 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 with the existing methods, the proposed tail-shortening approach leads to superior out-of-band emissions performance and a much lower error vector magnitude for the demodulated symbols.