Souljourner: Multiply the character's Level Adjustment by 3. When their ECL is equal to this number, they can reduce their LA by one ... but not for free. It costs them XP equal to 1000 times their ECL before the LA is reduced. Multiply any remaining LA by 3, and in that many more levels, they may repeat the process - until the character has a total level adjustment of +0.
For example: a Half-Dragon. Half-dragons have a level adjustment of +3 ... so at 9th level, the character has his first opportunity to reduce his Level Adjustment (and if he doesn't take it NOW, he can never lower his LA). At a cost of 9,000XP (lowering him to ECL 8), his level adjustment becomes +2.
This means he loses no class levels ... in effect, he "knocks one off the top".
Six levels later, at ECL 14 (with 12 class levels), he can do it again (3 times his remaining +2 LA is, of course, 6). He drops one LA, pays 14,000XP, and is now an ECL 13 character with 12 class levels.
Three levels after THAT (3 times his remaining +1 level adjustment), at ECL 16 (with 15 class levels), he removes the last point of level adjustment, paying 16,000 experience, and becoming an ECL 15 character with 15 class levels.
He has paid a total of (9K + 14K + 16K =) 39,000xp, and so, has earned 144,000xp - assuming he hasn't been crafting items, of course.
One of the benefits of this, is that he gains experience points at a slightly faster rate than his equal-lifetime-XP peers, because his average level keeps periodically dropping behind theirs by 1. Thus, by the time he's earned those 144K experience and is a 15th level character, probably, they are 16th level characters. The odds are, that in return for this added math, he will reach epic levels at roughly the same time as his peers.
The rationale behind this is that, as you go up in levels, less and less of your relative power is a result of your race ... but, level adjustment doesn't reflect that "diminishing return" if left constant. The difference between a Half-dragon Fighter(15) and a Human Fighter(15) isn't all THAT big - it's discernible, but not quite] a big enough gulf that the Half-Dragon should have had to pay 48,000 more experience (for a total of 153K) just to get there.
Using the Level Adjustment Reduction rules, a +3 race saves 9,000XP over the course of advancement to 15 class levels - and earns some of the remaining XP difference back too, in the form of being a level behind the average party level, when it comes time to hand out experience after every adventure.