This paper proposes a regional rate allocation method for enhancing the perceived quality in image compression. Bit allocation to image regions should be performed by considering the viewer's attention and distortion sensitivity maps in order to address subjective quality concerns. The paper first proposes an exponential model for the relation between the viewer's fixation duration and perceived information. The human visual system is more sensitive to the distortion around edges than the distortion in complex textured regions. Therefore, a novel distortion sensitivity method is also proposed that distinguishes true edges from complex textures without using edge detectors or gradient magnitude thresholds. The estimates for the visual attention level and the distortion sensitivity level are jointly used to modify the distortion contribution of each codeblock for determining its quantization parameter. The experiments validate the improved perceptual quality of decoded images due to the integrated use of the visual distortion sensitivity and the visual attention level in bit allocation. Moreover, the proposed bit allocation method is experimentally shown to yield a substantially higher subjective evaluation score than the other well-known bit allocation methods based on post-compression rate-distortion optimization, saliency maps, foveation of fixations and foveated just-noticeable-difference maps.