Wireless devices within an ad-hoc wireless network adaptively set their transmission power levels based on locally available information. Initially, each such wireless device sets its transmission power level to a relatively low level, and gradually increases its power level up to a predetermined maximum transmission power level. As the transmission power increases, the wireless device is able to incrementally connect with additional wireless devices located at increasing distances from the wireless device. As the wireless device connects with these additional wireless devices, it checks a connectivity constraint. When the connectivity constraint is satisfied, the wireless device stops increasing its power and operates at its current power level. In one embodiment, the connectivity constraint is a geometric connectivity constraint based on the angular distribution of wireless device connections. When a wireless device detects a change in the network topology, it repeats the power setting steps in order to adapt to the changed topology.