The following rules alter the recovery rates of natural and magical healing to some degree over the RAW (Rules-As-Written). Each DM is strongly encouraged to study them carefully before allowing them into their own campaign.
As written (in Swords & Wizardry), natural healing restores 1 hit point per day of uninterrupted rest. And four weeks of uninterrupted rest and recuperation will restore a character to full hit points, regardless of damage taken.
Extrapolating from this, we have integrated the following rules into our home campaigns. We call these rules, the Four Weekly Stages of Healing. They may seem complicated, but they're not. The progress of tracking healing this way is very simple and intuitive.
First Week: The character must rest uninterrupted. Any activities will re-open wounds and cause the character to begin to "bleed", losing 1 hit point per hour until the wound is properly tended to again.
Second Week: The character must rest, avoiding strenuous activities, or they will not regain any hit points for each day they are active. After the first week, a character also adds their Constitution bonus, if any, to the number of hit points they regain each week.
Third Week: The character may perform light duties and still recover hit points.
Fourth Week: The character can perform some strenuous tasks, but overexertion will negate the recovery of any hit points for that day.
Using magic to accelerate the healing process works as follows. Any day which a Cure (Any) Wounds spell is cast upon the character, automatically bumps that character's level of recovery up by one week, if they are not completely healed outright. This may only happen once per day, no matter how many healing spells are cast upon the same character after the first, unless the character is healed completely.
Efficacy of spells and potions are as follows. Each day, the first spell cast upon the character, or potion imbibed, will heal the character up to the full amount of hit points allowed by its type. Any further spells or potions are reduced by half normal. This reflects the fact that magic can only do just so much per day to restore a character's health.