Help with wood-burning stove issue?

My partner has removed her gas boiler and installed a solar thermal panel and wood burning stove, in which she has been burning FSC-sourced timber - the most recent load was beech, supposedly seasoned for 12 month. Unfortunately she still finds the stove pumps out a fair bit of darkish smoke coming out of the chimney. As she lives in a smoke control area, she needs to get the cleanest possible burn and the whole point of the exercise is to achieve the most sustainable, and affordable heating system. Any suggestions how she can reduce smoke output? Using very dry wood has been suggested, but she cannot verify the supplier's claim as to the dryness of the wood fuel... How would she go about testing moisture content of the wood? (in the absence of a lab, that is! :o)