To achieve high-speed (giga-bit) connectivity for shortrange wireless multimedia applications, the millimeterwave (mmWave) wireless personal area networks with directional antennas are gaining increased interest. Due to the use of directional antennas and mmWave communications, the probability of non-interfering transmissions increases in a localized region. Network throughput can be increased immensely by the concurrent time allocation of non-interfering transmissions. The problem of finding optimum time allocation for concurrent transmissions is an NP-hard problem. In this paper, we propose two enhanced versions of previously proposed multi-hop concurrent transmission (MHCT) schemes. To increase network capacity, the proposed schemes efficiently make use of the free holes in the time-Allocation map of the MHCT scheme; thus, making it more compact.