And in general, does an increase in the Load Index correspond to a decrease in pressure, or vice versa?
This is but one of the permutations that leads to confusion. I hesitate to answer your question directly because I know some folks will not remember this in its entirety - and that is important to do so. But here goes:
1) Standard Load on placard --> Standard Load for new tires: If the Load Index goes down, the pressure goes up and vice versa.
2) Extra Load on placard --> Extra Load for new tires: If the Load Index goes down, the pressure goes up and vice versa.
3) Standard Load on placard --> Extra Load for New tires: This is where it hits the fan.
a) If the Load Index of the placard tire is the same as the new tires, then add 6 psi to the placard pressure.
b) If the Load Index of the placard tire is higher or lower than the new tires, then the pressure listed on the placard +6 psi goes the opposite direction.
4) Extra Load on the placard --> Standard Load for New tires: More complication
a) If the Load Index is the same for both, then use the placard pressure minus 6 psi.
b) If the Load Index of the placard tire is higher or lower than the new tires, then the pressure listed on the placard minus 6 psi goes in the opposite direction.
If you have followed me this far, there are some other consideratons.
5) If the resulting pressure for the new tires is less than 26 psi, my personal recommendation is to use 26 psi. Inflation pressure helps hold the bead onto the rim, and there have been instances where severe manuevers have dis-lodged the bead.
a) Some tire manufacturers and others who give such recommendations say that you should not use anything lower than the placard pressure to maintain the original spring rate of the tire. This is an attempt to minimize the affect on vehicle handling.
6) Standard Load tires have a rated pressure of 35 psi (36 psi for metric based tires). If the resulting pressure for the new tires is more than that, then you need either an Extra Load tire or a larger size.
a) Extra Load tires have a rated pressure of 41 psi (same for metric based tires). If the resulting pressure for the new tires is more than that, then you need a larger size.
Please note: What is written on the sidewall of the tire may not be the rated pressure. The sidewall pressure would be the maximum usage pressure - and even then there are exceptions.
7) The above applies only to the current metric sizing sytem - the one that looks like this: P235/75R15. There are older systems that are expressed differently and those systems may or may not work the same. It is also possible that a future sizing system will be enough different that what I wrote above will not apply.
LT type tires are done similarly, but going between LT type tires and P type tires adds another layer of complexity.
As you can see, this is pretty complex - and I haven't even gotten into the mechanics of the calculation procedure - but the short version is matching the load carrying capacity of the placard tire at the placard pressure - and that requires load tables.
I hope everyone who reads this realizes that this is not a simple, easy to remember thing. Done incorrectly, you could be riding on dangerously under-inflated tires. It would be better not to remember any of this, rather than remember it wrong. Besides, you can always ask - you just have to be careful that the answer you get back is from someone who is an expert in the area.