soot indicates a design flaw. It could be that the fireplace opening is too large for the flue size, The firebox isn't designed properly, the chimney is too short/exterior chimney, or the house is so tight not enough air can exit through the chimney. Of these possibilities, by FAR the most common one is the height of the stack is too short.

Typically most chimneys are constructed to minimum code, which is inadequate for proper operation. By minimum code, I'm talking the 10-2-3 rule where a stack must terminate at least 3' above the roof where it exits, and at least 2' higher than any portion of the structure or roof within 10'. This code is a fire safety code for sparks and so on and not really a good one for producing proper fireplace performance. If the stack is an exterior stack this problem will be compounded and smelly downdrafts are likely to occur when the fireplace is not in use.

A properly constructed chimney is one which: a. terminates at least 2' above the highest portion of the home. b. at least 4' above the location where the chimney exits the structure.

Take a look at very old homes - where fireplaces were actually used frequently. These homes don't have problems with draft, they don't have soot staining the mantle, and they don't get downdrafts (unless someone has modified the original fireplace and chimney design during a remodel etc. of course). They also don't have chimneys located outside of exterior walls and they don't have chimneys shorter than the structure - at least ones designed for fireplaces (some chimneys on old farm houses etc. may have been used for cooking stoves etc. and they're smaller and may not follow these guidelines). Look at higher end older homes, pre-1950. the chimneys are tall, sometimes very tall, they exit from the roof usually inside the house envelope and they are higher than any other point on the home.

Unfortunately, today most "chimney professionals" or masons don't understand how to build a proper chimney and their most common canned and usually wrong response is "it needs a stainless liner!" If you purchase this home and attempt to correct the smoking problem, be aware that those who suggest a liner to solve the problem are likely incompetent and you need to keep looking for a competent mason/chimney professional. Good Luck!

Thank you so much for this incredibly informative post!

If the problem is that the chimney is too short, is there any chance it could be improved by adding onto the top to make it longer? Or would it be likelier to require a major overhaul?

The chimney absolutely can be extended and that is the only way to really solve the problem. The complications become: Cost, matching of the facing material (sometimes the same brick etc. is not still manufactured), and finding a mason to do it properly.