Can I close my damper a little so I lose less heat up my chimney?

This is a question that comes up periodically.  And, the answer is always the same:  NO!  Never do this.  The damper to your fireplace must be completely open when there is a fire burning.  If you close the damper, even slightly, you are running the risk of allowing smoke and other dangerous contaminants from the combustion process into the house.  And remember, the most dangerous by-product of combustion is carbon monoxide.  Always keep the damper in the fully open position until the fire and all coals have completely burned out.