I feel like I should back up the boat a little and explain that our first step in between what I described and a "normal" exchange" was having basically participants self-match. People signed up but then instead of being assigned a giftee, they had to claim it. So people who were fast, got what they wanted but everyone who prompted was required to participate and everyone got a gift. But invariably, I bet a few of those assignments were bad matches in the end simply because it was what was left, you know?