CSO (Compressed ISO) files are essentially ISOs that have been shrunk to save space. This was vital during the PSP's lifespan when Memory Sticks were expensive. Today, CSOs are preferred for storing large libraries on SD cards, though improper compression can sometimes cause stuttering in cutscenes or longer loading times.
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Purists often prefer playing on the actual PSP console. To do this, the console requires Custom Firmware (CFW).