Most modern wood heaters are attaining emission levels far below the EPA limit, some as low as 0.9 g/k and this shows the level of commitment the manufacturers have to their designs and manufacturing standards. Always check when buying a heater that it complies with these standards. There should be a compliance plate stating brand, model, serial number, efficiency rating and emission rating (i.e. passed testing for AS4012 and AS4013) In the past, when we were not concerned about such things, the air inlet control allowed for almost full deprivation of air to the firebox and this was often misused resulting in lots of smoke and creosote build-up because the fire would smoulder not burning off the solids in emission like it should.
These days the air is regulated so that even on the lowest setting, you will still have flame and the unit is burning cleanly for about ten hours or more.