Labyrinth Lord House Rule: Fewer Hit Points

Since YARPS isn't going to be ready for a true play-test for a few months, I'm going to be using Labyrinth Lord with a number of house rules for my soon-to-start online campaign. One of my gripes with B/X D&D and Labyrinth Lord (and, in fact, all editions of D&D) is that combat isn't deadly enough, particularly at higher levels. Several factors contribute to this problem, but the one that I dislike the most (and the easiest to address) is the high number of hit points characters have. So, here is my first experiment at a house rule to remedy the high number of hit points.

Fewer Hit Points
A House Rule for B/X D&D and Labyrinth Lord

All characters start with the maximum possible hit points at first level. Instead of rolling for additional hit points at each level, characters gain a fixed amount of hit points, according to their class' hit die, upon attaining even levels:

Hit Points per Even Level Attained by Hit Die
D4:  1
D6:  2
D8:  3
D10: 4

If a character has a CON bonus to hit points, it is only applied at first level and upon attaining even levels.