Mike Mearls recently confessed that the 5e design team is out of ideas for healing.
Here's my proposal for 5e healing. I'll call it the "Soldier On" rule.
In a short rest, you can bring your HP up to 2/3 of your max HP. Beyond that, your HP can only be raised through magic or through overnight healing. Overnight healing is old-school slow - say 1 or 2 HP per day.
Basically, the top 1/3 of your HP is physical injuries. The bottom 2/3 is energy, luck, and will. Your last 1 HP is a mortal wound. This is not too far from a wounds/vitality system except that it doesn't require you to maintain two different HP tracks: the only rule change from First Edition is that you heal up a little after a battle.
This rule allows injured characters to soldier on indefinitely, at slightly-reduced efficiency. You can swig the warm Gatorade of partial healing anytime, but the ice-cold spring water of overnight or clerical healing are luxuries not to be squandered.
The numbers could be tweaked depending on how serious you want injury to be. You could change the Soldier On threshold to be 50% or 75%. Ask this question: "At what stage of Hit Points depletion should we stop adventuring and go home?" and set the Soldier On threshold to a tiny bit above that.
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