Problem statement: Low complexity image compression algorithms are necessary for modern portable devices such as mobile phones, wireless sensor networks and high constraint power consumption devices. In such applications low bit rate along with an acceptable image quality are an essential requirements. Approach: This study proposes low and moderate complexity algorithms for colour image compression. Two algorithms will be presented; the first one is intensity based adaptive quantization coding, while the second is a combination of discrete wavelet transforms and the intensity based adaptive quantization coding algorithm. Adaptive quantization coding produces a good Peak Signal to Noise Ratio (PSNR), but with high bit rates compared with other low complex algorithms. The presented algorithms produce low bit rate whilst preserving the PSNR and image quality at an acceptable range. Results: Experiments were performed using different kinds of standard colour images, a multi level quantizer, different thresholds, different block sizes and different wavelet filters. Both algorithms considered the intensity variation of each colour plane. At high compression ratios the proposed algorithms produced 1-3 bpp bit rate reduction against the stand alone adaptive quantization coding for the same image quality. This reduction was achieved due to dropping of some blocks that claimed to be low intensity variation according to a comparison with predefined thresholds for each colour plane. The results show that the bit rate can be reduced by 72-88% for each low variation image block from the original bit rate. Conclusion: The results obtained show a good reduction in bit rate with the same PSNR, or a slightly less than PSNR of a standalone adaptive quantization coding algorithm. Further bit rate reduction has been achieved by decomposing the input image using different wavelet filters and intensity based adaptive quantization coding. The proposed algorithm comprises a number of parameters to control the performance of the compressed images.