Different trunked Private Mobile Radio (PMR) systems have been designed over the last several decades, all of which have symmetric downlink and uplink channel capacities. Due to this symmetry, these systems may not be spectrally efficient in case of different types of services, which are specific to PMR systems, such as group and broadcast calls. In this study, a new asymmetric trunked PMR system comprising a broadband, wide-area downlink and a narrowband cellular uplink, is proposed to achieve a higher spectral efficiency than current digital trunked PMR systems. This system is spectrally more efficient because in group and broadcast calls only a single downlink channel has to be allocated in the downlink part. However, as the number of clusters in the system increases, this advantage relative to PMR systems is lost, since the latter can employ frequency reuse. Spectral efficiency of the proposed asymmetric system (a-PMR) system and a standard TETRA system are compared using numerical case studies against different traffic loads and number of clusters. The optimum point, with respect to number of clusters, up to which the proposed a-PMR system is more efficient, is determined. It is shown that a very large PMR user population can be efficiently served using the proposed a-PMR system. The issues related to implementing such a system are discussed.