Light rail trim that matches your cabinets is commonly used to hide under cabinet lighting.

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I finally figured out what I need -but does it exist? LED undercab lights come 2 ways: an external driver/transformer that is hardwired or an internal/ integrated/housed one.. My kitchen is wired for an integrated UPLED. They are about 1 inch deep. Of course, I can get smaller (1/2 inch) external driver but that entails transformers (about 4) wiring, and undoing what we've done.
Does such a thing exist?
My cabinets are inset which dies not have space underneath, nor take a light rail.
Boring question, but appreciate help!!! Thank you!

Please can you do us a favour: take photos of your cabinets (face on), from the underside so we can see what you have and then open your cabinet doors and from there). There might be a solution...

Thank you-I may have figured it out but have more lighting questions.
From the photos you can see that I mocked up a box 1"X 4.5 inches (lengths variable) and put it on the underside of the cabinet box. I've spoken to the cabinet installer who will do the carpentry around the light box. The skin (white sheet ) makes the bottom of the cabinet totally flush--not inset on the cabinet bottom.
This would reduce the overhang of the fixture to 1/2 to 3/4 inches- which I could live with.
So on to the next problem. I had been planning to install Juno UPLED in warm white on dimmers. I went to a different shop yesterday, and the guy there said that the Juno LEDs had a problem with a noise that some/ not all could detect. He said the y recommend the Kichler LED which only comes in bright white. (It looked like a dental office) Another lighting supply place has suggested the LED Ruler -again bright white. So this latest fellow (30 yrs in lighting sales so he's seen it all) had me look at Xenon, as perhaps not the latest/ greatest, but something that was the same depth, no hum, and has a warm white and is 1/2 as much (again, on dimmer) I've read it creates some warmth but not like a halogen. What do you think of that?
The other recommendation he made was that I consider black rather than the silver cones in my recessed lighting. We have a view homes-mountains and city-bascially the whole point of the house, and he said that with the black cones it cuts done on the ricocheting reflection off the glass. (He was able to demonstrate the two and it seemed to be a marked difference.
Thank you for your advice!

another

sorry having difficulty with uploading the pictures!! Is this enough I took more

I had just installed LED lights that are warm - they come on a roll that you can affix according to the necessary length. You then add a plastic diffuser and the transformer can be put in the cabinet. The company I used was called LEDTEC (but I think there are others). They come in warm and cool lighting and even changing colour lights.

Sorry not to provide more helpful advice - I hope some other lighting specialists can step in for you.

Do you like Xenon under cabinet lights or perceive there to be a problem with them?

I prefer LED for many reasons - ecological, economical and cool (literally)