I would like to install LED deck light strips. The ones I would like to buy are adhesive backed strips. My problem is that the underside of my hatch covers and the area between the gunnel and deck are all carpeted.

I can't be the first faced with this and wondered what other guys did.

I did an install on my Strat last summer.

I would not install them on the underside of your deck lids unless you have to.  I think it is better to mount them inside the compartments, which is what I did.

If you install them on the lids the light shines right in your face while you are looking in the compartment.  You can't see anything in the compartment this way.  If they are in the compartment mounted up under the lip or pointed away from your position then they light up the compartment but you are not staring directly into the light and you can actually see.

The other thing with mounting them on the lids is that you are wearing on the wires/connection everytime you open the lid.  Its eventually goint to fail.  I mounted mine with the wires safe and out of the way through the side of the compartment.

I also would not place them on your gunnels close to your LCD as I have seen some do.  It makes reading the display more difficult at night.  I kept mine mounted back away from where I stand at the bow of the boat.  They are more back towards the console, so I get the benefit of the ambient light but I'm not staring right at them getting all the glare.

As for the gunnels, Id probably just use an exato knife or utility knife to carve out a piece of the carpet just large enough for the LED strip to fit and use clrear marine adhesive to seal he edge of the capet before positioning the LED strip.

Thanks for the tips, Hot Rod. I think I'll try them.

I agree with Hot Rod.  Do not mount the lights to your deck lid.  Also, I would suggest that you use red LEDs.  That way the lights will not affect your night vision.