While I can't claim to have addressed every losers bracket scenario perfectly, I think the latest update corrects a lot of the scenarios, especially for large brackets. There's no way to avoid rematches for some bracket sizes, but the "standard" sizes (4,8,16,32,64,...) and most variants should be smarter than before.
Existing tournaments will not be affected by this update, but all new tournaments and bracket generator output will reflect the new algorithm.
Special thanks to Pierre and Esteban for identifying some of the losers bracket seedings that didn't look quite right. I'm not 100% content with the changes this update enforces, but I think the algorithm is more reliable than the current one.
Thanks for using Challonge! There's plenty more to come, and I appreciate your support. Please feel free to contact me with your comments by following the Contact/Support link at the bottom of Challonge.com.