I thought of a good strategy too. Instead of throwing away that crude or common item, take it, then trash it. What this does is keeps it out of the items that you would get from loot dropped. If you keep taking/trashing all the loot you get instead of (in theory) recycling it back into the total loot, then this would increase your chances of getting better loot. If you understood that, I encourage you to try that out.
