There are MR16 LED lights which should fit in 3" cans.

The real question is whether the fixture will provide sufficient amount of light.

Thanks for the info. So my next question is, where do we find 3" cans?

Some manufacturers come to mind
WAC lighting
http://www.waclighting.com/USA/

You should be able to find entire solutions at either your local lighting store or online
For example
http://www.pegasuslighting.com/3inch-12v-mr16-halogen-recessed-lighting-housings.html

The only thing small about 3" lighting is the aperture. There is quite a bit of stuff (housing, power supply) that gets stored above the ceiling.

You may also want to look at csl lighting. They have 3" recessed led lighting that has quite a bit of output.

Here is a link that might be useful: CSL lighting