I'm assuming the tearout occurs when going from "across the grain", around the corner to "with the grain".
One thing you can do is start with an oversized piece that large enough to leave some wood on the waste side of the bit. This will minimize tearout.
Sometimes climb cutting will give better results, sometimes not.
As you've noticed, downcuts tend to tearout less, but not always.
If you're cutting rectangular shaped parts, here's one thing you can do.
rather than cutting around your part, do the cuts for each side separately. Do the crosscuts (across the grain) first, then do the rip cuts (with the grain).
The crossgrain cuts may need to be done in shallower passes to prevent tearout, but if you have plenty of extra width, it shouldn't be an issue.
There are a lot of subtleties involved that can affect the outcome.