Something like reducing the Will roll chances from 50% to 40% odds of triggering. That would've effectively included Noble Cause's current outcome -that of making it easier to chain missions together with a given soldier- while also making it more likely any given soldier would come out of any given mission not Tired, more directly reducing Fatigue crunch. I feel like this really should've affected the amount of Will soldiers lost within missions. Slot it in if you have nothing else of relevance to plug in, but only Resistance Orders capable of being outright useless (eg Impact Modeling after you've researched Powered Armor) are liable to be displaced by it. It can sometimes let you send your favorite soldier on three missions in a row where normally they'd end up resting from the second, but this is only a chance, and much of the time it will do, essentially, nothing.
Noble Cause is thus one of the lowest-value Resistance Orders. Noble Cause means multiple easy missions chained semi-close together are less likely to Tire your soldiers, but that's about it. Reminder that Will recovery per se does not affect how quickly soldiers recover from Tired or Shaken. Soldiers recover Will 20% faster out of battle.