A wireless network allocates uplink resources to wireless communication devices (WCDs) based on power headroom reports, with more resources being allocated to WCDs reporting greater power headrooms. Each WCD may determine a respective power headroom as a difference between its maximum transmit power and a transmit power requirement for its current uplink resource allocation. However, a WCD may report an adjusted power headroom that is obtained, for example, by decreasing its respective power headroom by an adjustment value. The WCD may then receive an uplink resource allocation that is based on the adjusted power headroom that it reported. The adjustment value could be based on a priority level of the WCD, a priority level of data to be transmitted by the WCD, and/or an instruction from the wireless network. In one example, basic-priority WCDs report adjusted power headrooms so that more uplink resources are available for high-priority WCDs.