Cutting small piece of (tempered) glass precisely?

I need to trim the glass diffuser for an LED light to fit inside a cabinet. I need to do it quite precisely and I have not been very good in the past using a standard glass cutter (either I have trouble scratching a precise straight line or it doesn't break smoothly).
The piece of glass is about 1/8 thick and 1.5 inches deep so I don't need to cut much. I only need to trim off about 1/4 inch (which makes using a hand-held glass cutter even harder). I'm pretty sure the glass is tempered.
Would a dremel with a diamond-coated rotary disc do a good job of making a smooth cut? (for example http://insidetrackclub.harborfreight.com/5-piece-diamond-mini-cutting-discs-31501.html )
Since the discs are so thin, I would hope to be able to make a precise cut by following the line and sneaking up on it as needed..
Would this work? Any other suggestions? ` Note: I tried using an angle grinder (with a metal grinding blade) and also a belt sander - but both of those approaches ended up more melting the glass (it got "yellow" hot) which caused it to crumble and ooze.
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Tempered glass will shatter when you try to cut it with a glass cutter. DO NOT TRY THIS.

Might work, but once you break through, they tend to vibrate, probably enough to shatter the glass.

Add a false bottom to the cabinet with a 1/4" deep rabbeted hole.

I think the belt sander sounds the best. Use a wet rag to cool the glass before it turns any kind of red. This will definitely take awhile. Be patient.
Glass dust is really nastyass stuff. I hope you're using goggles, a respirator with P100 filters, and a shop vac or dust collector.
How about a pic of the glass part? Are you talking about a glass in a washer shape or a tube shape?
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Doubt you'll have much luck, but take measurements first so you can get a proper replacement.
http://www.onedayglass.com/patterns.php Cutting Tempered Glass
We are often asked if we can cut glass that has already been tempered. Unfortunately, the answer to this question is no. All fabrication is done prior to tempering. That means we cut your piece to your exact specifications, drill and edge, and make all necessary customizations. Then we heat treat it in our unique vertical tempering furnace* and ship it to you.
Cutting Tempered Glass 1
Clean your tempered glass thoroughly and dry completely.
2
Place your tempered glass into a craft oven and set the temperature to 900 degrees F. Once the glass has reached this temperature, turn the oven off and allow the oven and the glass to cool for at least eight hours before removing the glass from the oven. This process is known as annealing, and it removes stress from the glass. The glass is no longer tempered.
Read more: How to Cut Tempered Glass | eHow.com http://www.ehow.com/how_4678952_cut-tempered-glass.html#ixzz1iuprcxBv It has to be annealed first.
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Tempered glass is made by spraying the hot sheet on both faces with water, which rapidly cools them and puts them under tension. It's this tension that gives the glass its strength. As soon as you weaken one side by cutting it, you release tension on the opposite side, and it shatters. Annealing solves that problem, but I have a feeling it's not practical for your project.
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On 1/8/2012 6:47 PM, Father Haskell wrote:

air.
its pretty hard to trim off a very small piece of glass without normal glass tools. take it to a stained glass place and they'd probably do it for free. it is usually done with a water cooled diamond glass bit, but can be done with SiC belts on a belt sander that you spray with a bit of water. if the glass is glowing, then it's WAY too hot and spraying water on it will probably shatter it.
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On Sun, 8 Jan 2012 15:55:09 -0700, blueman wrote

31
I work a lot with LED lighting and I don't really see a need for tempered glass (unless for safety), but you will soon be told it really can't be cut. Certainly standard glass will cut fine, but for thin strips you really need to have the same amount of glass on each side of the score line for success (i.e. always cut pieces in halves). What are the final dimensions you need?
-Bruce
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