Images that include halftone structures are sharpened. A copy of received halftone image data is blurred, thereby reducing a detectability of edges of the halftone structures. Edges remaining in the blurred image data are detected. An edge enhancement image is generated based on the detected edges. The original received halftone image data is combined with the edge enhancement image, thereby generating sharpness enhanced image data having halftone structures. The sharpness enhanced image data having halftone structures can be rendered through a halftone screen that is compatible with a halftone screen that was used to generate the originally received image data. Alternatively, the sharpness enhanced image data having halftone structures is rendered according to error diffusion techniques, such as, rank order error diffusion in order to achieve or maintain dot or halftone structure compaction.