Mr. Clean.

That's whom the Giants have been looking to draft in recent years. Players who have no rap sheets, no off-the-field problems, no history of injuries. If you were a team captain in college, even better. But it's clear from the last two draft cycles -- the two the Giants believe have been the most successful in recent years -- that the team puts a premium on character when deciding which players they should select.

They made a conscious move heading into the 2013 draft to be more risk-averse, to not take as many chances. They were always aware of players' backgrounds, but they didn't always weigh it as heavily in the war-room equations.

"I think we are always mindful of a player's character and background," general manager Jerry Reese said last week. "That always goes into the equation. It's not really anything new for us. Obviously, like all teams, we have taken some guys on the back end of the roster, more risk-reward kind of situations on the back end of the roster. We are very conscious and have been for a long time about backgrounds and character."

That, however, didn't stop them from picking players with red flags such as Marvin Austin and Jayron Hosley in the first halves of the 2011 and 2012 drafts, respectively. Those picks went bust.

So as the Giants head into this week's 2015 draft, they undoubtedly are looking into the type of person they will be selecting as fervently as they are the type of player they are picking.

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"We do all the background checks and our scouts go out and dig the information that we can," Reese said. "We interview them and try to put it all together and make a decision on it."

That's not to say whoever they take needs to be perfect.

"The thing you have to think about when you are thinking about these young players is that they are young," Reese said. "They do young-kid stuff. You can't just absolutely kill them. You wouldn't have anyone to draft. Kids do kid things and do college things and it happens. If a guy has a long list of issues, that is when you have to throw the red flag in there. Is this guy going to stop? If you have a couple things that college kids do, you can't just throw it away."

And of course, there are degrees.

"It depends on how egregious the off-field issues are, more than anything else probably," Reese said.

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There are plenty of young men in this draft who could wind up being solid NFL players but not solid citizens. There are others who have had run-ins with the law but have learned lessons and amended their ways. There even are some who have led stellar lives of impeccable virtue who could find themselves afoul of the law someday soon.

The Giants are trying to figure out which are which. But when it comes down to decision time, they'll lean on past performances on and off the field as the best barometer.

Notes & quotes: The Giants waived running back Michael Cox, a former seventh-round pick who suffered a broken leg last season. In two years with the Giants, Cox played in 18 games with one start and had 26 carries for 76 yards.