Two Weapon Fighting feat.

While this feat one of the best in the rules, the penalty to damage with the off-hand weapon is often overlooked, leading to confusion or strange on-the-fly fixes (such as the "well then the monster isn't really dead yet" scenario).

The penalty adds little to the game other than extra math and bookkeeping, so in these House Rules, character's with the Two Weapon Fighting feat ignore it. They can bring their full STR bonus to bear with either hand.