Gas and Oil Home Heating Furnaces - oil furnace is smoking

Hi all. I have a nice old oil furnace, in good shape, except that it it occationally smokes. We're checking it out and think we have determined what is wrong. If anyone has any additional info, please chime in. Here is what we're seeing:

- When the furnace shuts off, (i.e the fire stops) some oily smoke comes out of the burner assembly (air inlet vents) for a while.

- We think that the oil delivery assembly is dripping extra oil into the hot burner unit, which then heats up and makes the oily smoke.

Anyone have an experience like this? Is it a simple thing for the repair guys to fix?

Thanks to all!

(sorry if this is a double post. I had an issue logging in)

Have the burner serviced by your oil company or hvac company...Oil burners can be very dangerous.......