MP3 encoding quality is maximized by starting from the highest-quality source and filtering the extreme top end
MP3 reduces data by discarding audio it deems inaudible, and it struggles most with high frequencies. Key preparation: start from the highest-resolution source, not a previously encoded file; roll off the extreme top end before encoding (freeing bits for the rest of the spectrum); and leave a little level headroom since MP3 encoding can raise peaks and cause clipping. Judge the high-cut frequency by ear.
Examples
A mastering engineer rolls off the extreme top, leaves headroom, and exports the MP3 from the 24-bit session master rather than from a previously-encoded 16-bit file.
Assessment
Why does filtering the extreme top end before MP3 encoding improve the encoded result?