Getting Better

 I've decided to bump up the natural healing rate, to keep our AD&D characters playable with less down time.

• A full day's rest (24 hours) will return 3 hit-points.
• A full day's rest under competent medical care will give you back 5 hit-points.
• A single night (i.e an unbroken 8 hours) of undisturbed rest will return 1 hit-point, or 2 if under competent medical care.  Note that three 8-hour stretches of rest makes a single day, so would give you the full 3 points for a day of rest, or 5 if under medical care.
• A day of broken rest, in which no further damage is taken, will still return 1 hit-point.

 This is going to be more relevant at low levels than high, of course.

Saving Throws -- house rule

I'll be using the regular Saving Throws as per their category names — i.e. Paralyzation, Poison & Death Magic vs. paralyzation, Breath vs. breath weapon or other area-effect attacks, etc.

However, for more general-purpose saving throws, such as clinging to a tiny crack in a cliff face to avoid plummeting to a horrible splatty doom, I will generally just use characteristic saves — STR, DEX, CON etc. — because I can't be bothered remembering which of the BtB saves are supposed to be used for each of those. I will graciously allow the PCs to add +1 to their CHAR saving roll for every band of 3 levels* they have, because I'm a big old softy.

They also get another +1 for saves based on their primary stat of their character class — i.e. on STR rolls for fighters, INT rolls for wizards, DEX rolls for thieves, etc.

• * i.e. +1 for levels 1-3, +2 for levels 4-6, +3 for levels 7-9, and so forth.