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When implementing an appropriate windowing, the interference from a Cognitive Radio (CR) system to licensed systems (primary users) will be significantly reduced. Consequently, power allocated to subcarriers can be increased, especially subcarriers having far spectral distance to primary user bands can be allocated full of its maximum possible power. In this paper, we propose a new class of sub-optimal subcarrier power allocation algorithm that significantly reduces complexity of OFDMA-based CR systems. Two sub-optimal proposals, called Pre-set Filling Range (PFR) and Maximum Filling Range (MFR) are studied. Investigations show that this new power allocating algorithm allows CR systems obtain high throughput while retaining low complexity.