If the person is someone beneath you at work, or someone you don’t care about (skip the rest of this paragraph if it’s not), you could make a bit of a joke about it. For example, the very next time he or she talks too loudly, tell them immediately. If they do it again, tell them again. Get everybody involved in this, so that they see it is not only one person who is bothered by their loudness, but everyone. Do it in a way that isn’t snippy or mean. If he or she doesn’t take it seriously, laugh along then explain that you are serious and seriously annoyed. Remain diplomatic and polite, but firm. If the person takes offense, explain that you aren’t trying to pick on them or anything, but that it does affect your concentration. If the person takes it well, keep reminding her every time she raises those decibels, because she probably doesn’t even realize when it’s happening.
However, if the person is in a position of power at your job, if they didn’t take it well the first time, or you can’t stand the thought of hurting their feelings… then don’t, and instead, just use The Incognito Help Line to tell them to tone it down. At the end of the day, this needs to be followed through on and it’s more important that they get the message, regardless of where it comes from. So it’s best to let The Incognito Help Line tell them for you, so you don’t have to. Your ears will thank you the moment you do.