In this paper, we introduce a new mixed priority scheme that utilizes the logarithmically equi-spaced random transmitter power levels (LESRTPL) model to control the assignment of the transmitter power levels, assigned to each priority class, adaptively. Packets, of different priority classes contending simultaneously over the WIRELESS channels to capture a contention slot, will transmit using LESRTPLs set pre-assigned to them using an adaptive prioritized controlled capture (APCC) scheme. Higher priority classes are assigned stronger power levels according to their priority index and the estimated number of backlogged packets on the frame. The WIRELESS channel capture model includes Rayleigh fading, shadowing, and path loss. The throughput of the algorithm is analyzed and its delay performance evaluated using simulation models. Results show that the new priority scheme offers significant improvement to the throughput and the waiting time of the different priority classes over Basic Aloha Algorithms, especially to high priority class packets.