Once you've been given an artefact or a relic, the game increments a counter. What you then do with the artefact doesn't matter; you can keep it, sell it, or throw it away, but the counter will remains at its new value. And once the counter reaches its limit (I can't remember what that is for this game), the game won't give you any more. This doesn't apply to "placed" artefacts, of course.The only way of getting the artefacts and relics that you want is to abandon the positions that give you those you don't want. So when you kill a high-level monster, save the position before you loot it. So if you don't like what you get, you just reload the savegame. 
In these Taverns, it's called "mephistoing" after Mephisto, the player who first publicised the technique.
