car has recently been emitting smoke.

Low compression will make an engine run uncommonly smoothly. Rough running is usually caused by a misfire, and that's what should be diagnosed. How long since the spark plugs and wires were replaced? Other than that, I need test results to analyze. I also need to know the color of exhaust smoke to determine the cause. It could be white, blue, or black.

White

White smoke from the exhaust is a sign of burning engine coolant. That is caused by a leaking cylinder head gasket. Your mechanic can perform a chemical test at the radiator that will confirm a leaking head gasket about 95 percent of the time. You can also add a small bottle of dark purple dye to the coolant, then search a day or two later with a black light. The dye will show up as a bright yellow stain that you can follow back to the source. If the head gasket is leaking, you'll find the dye inside the tail pipe.