You would be looking at t4 fluorescent lighting which may just protrude. There are hard wired led lights that are ~ 1/2 inch high. For example the eW profile powercore strips from Philips.

Nearer the front of the cabinets. Ucl fluorescent will have the ballast contained within the housing. Since the light portion is about 3/4", the only way to fit the space is to lay the light on its side. Some manufacturers do just that. Even if you mount the fixture towards the back, the bulk of the housing makes the position of the tubes nearer the front.

There will be a shadow zone due to the physical characteristics of having the light lying on its side.

Thanks you so much, davidtay, for responding. I've read many of your lighting posts and was hoping you would help me out. I found some T4SuperSlim ones from American Fluorescent that might work? It says they're less than an inch wide and easy to install with mounting clips, hardwire or plug in. Does that mean it has no box to go in a cabinet? Later down in the dimensions it says they are 1 1/4 or 1 5/16 inches high. That means after they're installed, they'll be too big?

Also, will a T4 give enough light as opposed to a T5?

Will the shadow zone be a major problem?

Do I want a warm or cool lamp? Don't want the bright blue or pinkish/yellow lights. What is "normal"?

Thanks so much for your help. This is only my second time to post on GW, but I'm on here everyday looking for help with our kitchen redo.

Do you mean transformer/ power supply when you say box? Direct wire fixtures do not have a need for a power supply.

The t4 will be sufficient for counter top lighting.

The shadow zone is more of an aesthetic issue. If you have the fixture installed such that the tube faces the backsplash, there won't be any shadow at the top of the backsplash. However, there will always be some shadow regions between the light fixtures.

You may find the following sites informative.
http://www.saunterlighting.com/
http://www.slimfluorescent.com/
http://www.colorkinetics.com/ls/essentialwhite/ewprofilep/

As for the light color, that's a choice you need to make. There are 2 camps
1. The color of the Ucl needs to match the general lighting.
2. The Ucl can be more intense/ whiter.

Warm white typically means 2700k. Neutral white ~ 3500k -4000k and daylight white is ~ 6500k. Daylight white will have some blue. Warm white will be slightly yellowish.

The height quoted has the ballast at the top. Yes, that will protrude.

Thank you again for replying. DH and the electrician conned me into agreeing to hardware the lights individually so they have to be manually turned on one by one. I think the electrician didn't want to go up in the attic in our 105 degree heat at the time and DH saw extra dollar signs. So now I have more questions, of course:

1. According to your two links, they can come with on/off switches on each fixture?
2. Do I need two-prong or three-prong or does it matter if they're not going to be linked together?
3. I was talking about a hardwire box with or without a switch--included in the accessories section. Since I won't have one wall switch to turn off/on, do I need the box? I was thinking I had read somewhere that they were so small they didn't have room for all that to be included in the unit, thus the need for extra parts. So I need absolutely nothing else other than what comes in the package?
4. I have a 36- and three 30-inch cabinets. What lengths do I need? One 29 and three 21s or one 34 and three 29s?
5. And in my earlier reply I asked about the size of 1 1/4 inches protruding, but I was confusing height with width since I'll be putting them on their sides. So the 3/4 or 7/8 is what I'm concerned about. Looks like that area is ok.

Again, thank you so much. I don't think our area lighting store has these, although maybe they could get them; but I hesitate to ask all these questions of them and then turn around and order online.

You may want to look at the offerings from Kichler.

The light fixtures need to be designed such that the light lays on its side. Otherwise, you need to figure out how to mount them and how to change the tube and ballast in time.

The savio lighting micro fluorescents come with individual switches on the body as do some other brands.

The number of prongs depends on the light chosen. The 3rd prong is for the ground wire.

The lengths needed depends on
1. The availability of uninterrupted flat cabinet space.
2. Whether you intend to have a continuous run of lights, fitted end to end.

I think you would be impressed by the uniform illumination and ease of use when you've seen a continuous run of Ucl in operation. However, a continuous run requires extensive uninterrupted flat cabinet bottoms (no fences) and usually a wall switch.

Not having a wall switch also means that the power has to be turned off at the breaker when you replace the ballast. In the future, if you decide to replace the lights with dimmable lights at some point in the future, you will need a location for a wall switch.