This paper formulates a new problem for the optimal placement of Unmanned Aerial Vehicles (UAVs) geared towards wireless coverage provision for Voice over WiFi (VoWiFi) service to a set of ground users confined in an open area. Our objective function is constrained by coverage and by VoIP speech quality and minimizes the ratio between the number of UAVs deployed and energy efficiency in UAVs, hence providing the layout that requires fewer UAVs per hour of service. Solutions provide the number and position of UAVs to be deployed, and are found using well-known heuristic search methods such as genetic algorithms (used for the initial deployment of UAVs), or particle swarm optimization (used for the periodical update of the positions). We examine two communication services: (a) one bidirectional VoWiFi channel per user; (b) single broadcast VoWiFi channel for announcements. For these services, we study the results obtained for an increasing number of users confined in a small area of 100 m2 as well as in a large area of 10,000 m2. Results show that the drone turnover rate is related to both users’ sparsity and the number of users served by each UAV. For the unicast service, the ratio of UAVs per hour of service tends to increase with user sparsity and the power of radio communication represents 14–16% of the total UAV energy consumption depending on ground user density. In large areas, solutions tend to locate UAVs at higher altitudes seeking increased coverage, which increases energy consumption due to hovering. However, in the VoWiFi broadcast communication service, the traffic is scarce, and solutions are mostly constrained only by coverage. This results in fewer UAVs deployed, less total power consumption (between 20% and 75%), and less sensitivity to the number of served users.