What is more ironical about "clean" bitcoins, is that some exchanges consider bitcoins "tainted" after a recent mixing process.
You can just make a few hops (transactions) to other addresses you have, to make that mixing undetected by exchanges.
If I remember it correctly, somebody said their mixed coins were classified as tainted even though they already move them through some addresses. So some exchanges might trace back to more than just one past transaction to see if your coins are "bad" or not. Although if you use a mixer that doesn't really make it hard for exchanges to see that you use them is a bad idea to begin with.