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If your printer is badly tuned, then these parts will have a very loose or very tight fit. And by tuned, I am mostly referring to how much plastic the extruder is extruding as well as the retraction/deprime. You can look at the broad flat sides of the printed case as an indicator. The smoother the sides, the better tuned the printer is.
I would guess that your printer is far from in-tune, and is not extruding enough filament. Decreasing the filament diameter when slicing will increase the extruded amount. Beyond that I can't really say what you should try since I don't know what kind of printer you are using, what software, etc. And even if I did know these things, unless you happen to be using the same stuff I have then I would be less than useful.