I have seen advice on pruning relatively young shrubs but nothing on a mature speciman.
When looking at the photo of your Smoke Tree (Cotinus coggygria) enlarged, it appears to be the green, rather than the purple, variety. According to the Connon Nursery catalogue (2009), it has reached about its maximum size; 3.5m high, and 3 m wide. Some of the varietals, such as “Royal Purple” or “Young Lady” are smaller, with a mature height and width of 2.5 m. Either way, this species has a rangy growth habit, and should be pruned yearly to maintain a more compact shape. As your smoke tree is mature, and has multiple branching low to the ground, it is really a shrub, and should continue to be pruned that way. Choosing a leader to encourage growth as a tree now, is not recommended.
Smoke trees are a summer flowering shrub, that is, produce flowers on new growth. That means they should be pruned in the late winter or very early spring, while dormant. One advantage of pruning at this time is that the shape and branching can easily be seen. All good practices in pruning start with removing dead and broken branches with a clean, sharp secateur or lopper. If the branches or trunks are large, use a clean, sharp pruning saw. Next, if there are crossed branches rubbing each other, gauge which branch is best to keep, and remove the other one. Rubbing branches can introduce pest and disease. Now also is the time to remove weak branches, suckers from around the tree, and any water sprouts – those long branches that stick straight up and don’t branch on their own. When pruning any shrub, always cut to about 1cm from a growth node, or where buds are evident – that is where the new branching will occur. If it’s a trunk or large branch cut only to where the collar of the branch meets the main stem.
Next, decide how high you want to maintain this shrub. Branches can be pruned to that height over the next two years. Chose half the branches to prune this year, from all areas of the tree (that way is doesn’t look lopsided after pruning) and cut them to a growth node below the approximate height you want. Next year, these branches will have grown, but the branches left alone can then be cut back to the desired height.
Now the entire shrub is at the height you prefer, and should be maintained yearly to that height. This article also suggests that if the smoke tree is too rangy, it can be pruned to just above the ground in late winter, to maintain a tighter growth. I have done this with other shrubs, such as dogwood, to good effect, although I have not done this with Cotinus.