Efficient exploration strategies are vital in tasks such as search-and-rescue missions and disaster surveying. Unmanned Aerial Vehicles (UAVs) have become particularly popular in such applications, promising to cover large areas at high speeds. Moreover, with the increasing maturity of onboard UAV perception, research focus has been shifting toward higher-level reasoning for multi-robot missions. However, autonomous navigation and exploration of previously unknown large spaces still constitute an open challenge, especially when the environment is cluttered and exhibits large and frequent occlusions due to high obstacle density, as is the case of forests. Moreover, the problem of longdistance wireless communication in such scenes can become a limiting factor, especially when automating the navigation of a UAV fleet. In this spirit, this work proposes an exploration strategy that enables multiple UAVs to quickly explore complex scenes in a decentralized fashion. By providing the decisionmaking capabilities to each UAV to switch between different execution modes, the proposed strategy is shown to strike a great balance between cautious exploration of yet completely unknown regions and more aggressive exploration of smaller areas of unknown space. This results in full coverage of forest areas in multi-UAV setups up to 30% faster than the state of the art.