Recessed Lighting in Finished Basement

I'm currently in the process of finishing my basement. I want to use recessed lighting, but wasn't sure how to install. It is approximately 9' from the concrete floor in the basement to the bottom of the floor joists on the ceiling. I plan on using a drop ceiling at about 8' so I don't have to frame around any obstructions. That means it will be approximately 1' from the bottom of the floor joists to the ceiling tiles. I haven't found an recessed lighting that has an adjustable height so the light could be mounted to the floor joists but hang down far enough to be flush with the drop ceiling.

Do I have to build some sort of frame to install the recessed lights in that hangs down from the floor joists above?

 

Either buy recessed cans with hanger bars (Halo) or buy the hanger bars for your cans. The bars extend out and clip to the main bars for the extended ceiling. You will need to run some sort of flexible cable to the fixtures in a manner that is compliant with code in your area.