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It's all about dielectric strength. Smaller size caps have much less dielectric, thus the voltage required to punch through the dielectric is much lower. So, with everything else being equal, a smaller capacitor will have a lower rated voltage than the larger capacitor.
Well, you first have to indentify what kind of noise you have, then determine what value of capacitor you need, then see if that capacitor is available in smaller sizes. Remember that most of the higher dielectric materials vary considerably over temperature, so you'll have to take your temperature operating range into account.
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