Power consumption has been a significant issue for many mobile and wireless devices, especially those with high rate applications. This paper presents a methodology and framework to minimize system power consumption for multichannel communications using cognitive radio (CR) based on the application quality of service requirement, the channel condition, and the radio capabilities and characteristics. The CR framework enables an adaptation process that is aware of the radio (component) capabilities and characteristics. This paper mathematically formulates a system power consumption minimization problem under a rate constraint for multichannel communications and develops numerical solutions. Simulation results show that the knowledge of the radio capabilities and characteristics can help to reduce system power consumption significantly (e.g., up to 55% for a multichannel system with Class A power amplifiers).