Situations like this should be remedied as quickly as possible in a match to avoid future complications.
When plagued by an unfortunate sequence of next pieces, an overhang is another form of a scapegoat.
A player should be aggressive when the opportunity arises. Do not sit and counter garbage. Let yourself receive garbage and send it back. You want to send the most garbage as possible. Often, it's better to tetris after the opponent because they will not be able to counteract the garbage, either accidentally or intentionally.
If you have a chance to BtB in a short time period, don't pass it up. The more time you give your opponent between a BtB, the more likely he will have formed a plan for the upcoming garbage.
When nearing a top out, counter the garbage as best as you can. Your opponent will not recieve extra ammunition and will have to build his own tetrises. Do not waste time making many singles. Most of all, remember not to overstack.