Blast-cleaning systems are disclosed, which enable a single system to handle different classes of particulate blasting media, such as grit, powder, and dry ice, and to deliver controllable mixtures of different media types during a blasting operation. This “multi-media” system includes a hopper having two chambers or other supply assemblies that are isolated from each other, for holding two different types of blasting media. Both chambers provide their particulates to a metering control device, which supplies a compressor. For example, by combining grit with dry ice, extremely efficient cleaning can be accomplished, with greatly reduced production of solid waste. Tests have shown that combinations of dry ice (at roughly 90%) with a grit or powder can provide far greater cleaning efficiency than either media type by itself.