Round 2, Pick No. 62: Irv Smith, TE, Alabama
Though the Saints did pick up Jared Cook in free agency, which I believe was a great move for them in terms of giving themselves the freedom to pick best player available with their early pick -- which was very needed since they only have one selecting in the Top 150 -- I don't think the addition(s) to the tight end position should stop just because Cook is there. Cook is 32 years old, and I would rather stay ahead of the curve, in that regard, as opposed to risking falling behind it.
The Saints need to be all-in on making Brees' final years at quarertback as good as they can be. They cannot afford to sell themselves short in terms of talent and options at any level. By throwing Smith in the Saints' current tight end group, you're sure to have a passing weapons each week, even if injuries or late-season fatigue start to set in, keeping the Saints tough to stop, as they were for most of last season.
Round 5, Pick No. 169: Hunter Renfrow, WR, Clemson
The Saints do not pick again after No. 62 until pick No. 169 in the fifth round. They could be a team that does some trading back with that first pick to perhaps pick up a couple more draftees, but there's a chance that the other side of things could weigh more, knowing they have so few picks at the top (one) that they have to use it and make the most of it.
Whatever they do there, they'll certainly need to pick players with higher impact potential in the later rounds. As a player who is a separation nightmare for defensive backs with quick feet and a natural ability to make catches through traffic, Renfrow could be that player, especially with Brees throwing him the ball. If those two get their timing down, they would be very tough to stop in the short areas.
Round 6, Pick No. 178: Austin Bryant, EDGE, Clemson
Alex Okafor was a decent-sized loss for the Saints along the defensive line this free agency period. They signed Mario Edwards to try to curb that loss, but I think some draft resources need to be thrown in there, as well.
Bryant makes sense for them because I don't see them investing too high of capital in that area with both Cam Jordan and Marcus Davenport already solidified as the starters, but coming from a successful and experienced line at Clemson could lend Bryant to being a key rotational player in New Orleans pass rush arsenal.
Round 6, Pick No. 204: Jimmy Moreland, CB, James Madison
I am a big fan of Moreland. This is a player who is just 5-foot-9 and about 170 pounds, but he talks a mean game and he backs it up. At James Madison, Moreland was a lockdown cornerback, even at his size. He would cover players in the slot and on the outside, and his ball skills and knack for taking interceptions to the house for six points speak to the mentality he has as a defensive back.
Not only do I think he would fit perfectly into a slot need the Saints have, he would also be a perfect culture fit.
Round 7, Pick No. 233: Lamont Gaillard, OL, Georgia
Though not a major need since the unit played well last year, as a whole, you can always stand to pick up offensive linemen with potential to develop and allow them to be swing/rotational players in their early years. Gaillard will be one of the more coveted offensive linemen for such a role later in the draft, but the Saints are one of the teams that could use him.
Round 7, Pick No. 246: Jamal Custis, WR, Syracuse
Custis was dominant at the East-West Shrine event this offseason in St. Pete, FL, and for that I think he is a player who will get drafted. He's smooth for a big man with good feet and had reliable hands catching through contact. Do the Saints need another receiver? No, not really. But you know they'll always take flyers on ones later in the draft to keep the passing attack fresh while looking to hit the jackpot on one.