I don't suggest picking up any closers until at least after round 10. There are plenty of good closers left later in the draft.
Yes you're gonna miss out on Gagne, Guardado and Wagner types but the opportunity cost of getting a closer that early is way too high. You can win the saves category by having a bunch of relatively good closers as opposed to having a couple guys like Smoltz and Gagne.
Trust me, there will be at least 10 closers still available for you at round 8. I guarantee it.
Good starters don't last later in the draft, good closers will.
Here's what I would do. Figure out how many keepers you get for next year, and then take that many players as position players or stud pitchers. Then take your relievers after you get a solid core of players. Because in any given year, half the closers lose jobs.
So if you've got an 8-keeper league, pick your first closer around round 9. Then if there's a good one left in the 10th take him.
I'd hate to spend two early round picks on closers, and then have bubkis left when trying to select my keepers for the following year.
I understand your opinion, and that is usually my strategy, but that works better for smaller leagues. Since there are 15 teams, with each team having 4 RP spots, that would require 60 closers to be available. I think they might go rather quick, and I'm just trying to prepare myself. If I can get 2 solid closers, then I don't plan on picking up my closer sleeps until after round 20.
Also, I've found that I can usually trade a stud closer midway through the year, for some decent value to fill some other holes on my team.
There are 6 keepers, so that is why I would pick one of the 4 stud closers in the first 4 rounds. If I get Gagne, Foulke, Rivera or Wagner, I would consider them a keeper. Then around round 10 I would pick up a second good closer.
For my keepers next year, I'm hoping for a stud closer, stud pitcher, and then 4 position players.