Many people do not associate the word "Puritan" with evangelism. It is hard to imagine John Owen button-holing someone outside of Parliament asking, "If you died tonight, do you know if you would go to heaven?"
J.I. Packer has a helpful chapter on Puritan evangelism in his book A Quest for Godliness:The Puritan Vision of the Christian Life (Crossway, 1990). If we would adopt this philosophy, the result might be fewer "decisions" but more actual conversions; smaller churches, but holier ones.
To their [the Puritan preachers] minds, it would be the worst advice possible to tell a troubled person to stop worrying about his sins and trust Christ at once when that person had not yet faced the specifics of his or her own sinfulness and has not yet come to the point of clear-headedly desiring to leave all sinful ways behind and be made holy. To give this advice, they held, before the heart is weaned from sin would be the way to induce false peace and false hopes, and so produce ‘gospel-hypocrites,’ which is the last thing that a Christian counselor should be willing to do.