One of the interesting changes in the new player agreement is the limit on compensation for draft choices. This places a limit on what each team can spend on their draft picks in the first 10 rounds. Exceed that limit and there are fairly stiff penalties. Stiff enough that very few, if any, teams are going to exceed them and the Twins will certainly not be one of them.
The amount a team can spend depends on their position in the draft and includes consideration of compensation picks. So the Twins should have a relatively generous budget. At least compared to other teams. The budget, however, is allocated by draft spot. If they fail to sign a player their budget is reduced accordingly. In other words they can't not sign a choice and use the money elsewhere. They can however pay someone less than budgeted for their draft spot and spend that money elsewhere. So the Twins could pick some guys who are easy to sign with their compensation picks. They could then use the money to sign their top choice or sign players they take later who dropped because of signability issues. Of course the players' agents are going to figure out what slot money is and it may be tough to get a player to take less than the budget for their draft position.
Because of the budget constraints, players who want over slot money are unlikely to be taken later in the first 10 rounds. But the budget limit disappears after the 10th round. That means that starting with the 11th round there may be some very good players available who in the past would have been taken earlier and paid over slot to sign. With the second choice, the Twins will get to choose from the best of those players. Depending on their own budget decisions, they could pick up a pretty good player that normally would have gone a lot higher.