All of mine were by-products of other hunts with buffalo as the primary game animal. However, on my first trips, which were primarily for plains game, I had no interest in them. I easily could have acquired a permit for Damara Dik Dik on any of several trips to Namibia and didn't because I couldn't fathom hunting an antelope the size of a rabbit.
I shot a steenbock in Namibia that we used for leopard bait without even thinking about declaring him a trophy and taking him home.
It wasn't until I managed a long and ultimately successful stalk on an Oribi in Mozambique that stretched the barrel of my S2 Blaser a bit, that I realized what wonderful creatures these things were.