Voice over IEEE 802.11 becomes much more cost effective when deployed over IEEE 802.11-based Wireless Mesh Network (WMN) due to the license-free backhaul wireless links. However, medium access control (MAC) based on IEEE 802.11 traditional random backoff protocols that are suitable for throughput-sensitive data services cannot satisfy the performance of voice services. Therefore, in this paper we propose an improved MAC based on medium reservations, called EMDA. EMDA improves significantly the optional Mesh Deterministic Access (MDA) MAC, to provide a much higher voice call capacity thanks to voice packet aggregation feasibility and much less MDA signaling overhead. EMDA is based on a per-node reservation of a block of contiguous transmission opportunities that are properly dimensioned. Moreover, we further improve the near-deterministic access of EMDA by using short jamming periods just before these reservations. Extensive simulation results show that our proposed MAC enlarges the voice capacity and uniformly distribute it over the WMN. It also provide a better performance in guaranteeing hard delay constraints, lower jitter and lower packet losses compared to other MAC.