The Player's Handbook says in the section about Damage
When your attack succeeds, you deal damage. The type of weapon used (see Table 7–5: Weapons, page 116) determines the amount of damage you deal. Effects that modify weapon damage apply to unarmed strikes and the natural physical attack forms of creatures. Damage reduces a target’s current hit points.
Minimum Damage: If penalties reduce the damage result to less than 1, a hit still deals 1 point of damage.
Strength Bonus: When you hit with a melee or thrown weapon, including a sling, add your Strength modifier to the damage result. A Strength penalty, but not a bonus, applies on attacks made with a bow that is not a composite bow. (PH 134)
I know a creature can take a -4 penalty to inflict nonlethal damage with a weapon that inflicts damage, but is there a rule that permits a creature to voluntarily reduce the amount of weapon damage he inflicts? For example, can a creature choose to employ less than its full Strength when making an attack?
Best Answer
Not Explicitly
There are effects that halve incoming damage, that lower damage taken, probably even that lower damage done, but they are all spells and magic items and whatnot.
The default assumption of an 'attack' is that you are swinging as hard and as fast as you can.
A creature can use weaker weapons (such as an Unarmed Strike, or a Gauntlet) to deal the damage - light weapons only do half strength on damage.
If you did want to do less damage, though, 'pull' your swing, I don't see why you couldn't do that as a houserule. I'd say it's hard to pull your swing, so it'd be a -4 to hit. I'd also say that it would be a bluff check to conceal your 'pulled' swing from others. It'd be reasonable to swing for half, or to swing for say, a quarter (light and 'extremely light' hits), but not to dictate the exact amount of damage it does - with a longsword and +3 STR mod, for example, i'd say swinging for 1d4+1 (half) or 1d2 (quarter) would be fine but swinging for exactly 3 damage wouldn't be allowed.
Pretending to swing but not actually hitting or doing damage (just a touch attack) is more along the lines of a Bluff check straight up.