What you need:
- Scissors
- Cardboard (preferably on the thin side)
- Duct tape (or some other form of strong tape)
This image shows what I mean by thin cardboard. It was taken from a plain shoe box. I only say to use thin cardboard because it is easily foldable into small shapes, unlike thicker cardboard.

Those scissors are nothing special, just from my roommate's kitchen knife kit. He won't mind.
The next step is to separate the (black, in this case) bezel from the power panel, by pushing down the tabs and pulling out the bezel, as depicted below:

The tabs on the other side should slide right out since they are no longer under any force to stay in place.
The inside of the bezel should look like this, with the red LED casing being the lower of the two shown:

You will want to bend the cardboard around the LED casing; it works best just folding it into a square. I suggested using duct tape because it is strong enough to be used in a thin slice, as will be needed here, to hold the cardboard in its form around the LED casing.
It should look like this when you have the cardboard on the casing:

Notice that the cardboard is taller than the casing. This is because the LED does not actually fit inside the casing, but sits on the end, so the cardboard actually needs to be tall enough to surround the casing and the LED. This will take some trial and error - I need about 4 or 5 different cut outs before I got the right size (this is where the patience requirement kicks in). When completed, simply put the bezel back on and it should fit snug and look like this:

Don't worry, you can't see the cardboard from outside the case - it's too dark to see it without a flashlight shining directly on it, especially while the case is running.
Below is the final product, one picture with the red LED on by itself, and one with the blue LED on to show that it is indeed still bright enough to be seen. (I apologize for the graininess, but had I used a flash you wouldn't be able to see the LEDs...)
And it's just that simple!
Addition on 5/8/07:
When I was removing the front panel switches so that I could sleeve the wiring, I decided to also add cardboard around the blue LED casing, as shown in the next picture:

There was no noticeable difference versus before with only cardboard around the red LED casing, so if you are going to do this "mod" it really is only worth the time to do the first part.