Setting whole resolution levels of coefficients to zero can be very useful. For examples, one can construct a linear smoothing method by setting all coefficients above a particular resolution (the primary resolution equal to zero. Also setting particular levels equal to zero can also be useful for removing noise which is specific to a particular resolution level (as long as important signal is not also contained at that level).
To remove individual coefficients on a systematic basis you probably want to look at the threshold
function.