A set of methods, techniques and hardware is described for compressing image data for memory bandwidth and memory storage reduction in graphics processing systems. The disclosed technology can be used for compressing image data sent to the frame buffer and/or image data residing in the frame buffer. The compression process can be based on an adaptive number of base color points and an adaptive number of quantized color points. An adaptive technique for compressing alpha values based on pre-calculated maps or using an estimated alpha value based on thresholds is also disclosed. An implementation of the disclosed methods has, for example, a low hardware overhead, low buffering requirements, and low and predefined compression latency. Also, the disclosed methods allow, for example, random accesses to compressed image data.