When a harsh phrase like “grievance hearing” enters the conversation, it’s not easy for both sides to get past the hard feelings and tough talk to work a deal.

That the New Orleans Saints and Jimmy Graham — who is now and forevermore a tight end, amen — were able to strike an accord on a new four-year contract is really a remarkable achievement. Consider the initial wide monetary gulf between them and the hot debate over what position he actually plays, plus Tuesday afternoon’s looming deadline, that would have forced a franchise tag to be stapled to Graham’s No. 80 jersey.

Nobody wanted that. The franchise tag would have left Graham poorer, as it turns out, in the long run and vulnerable to the possibility that an injury could have eroded his enormously lucrative earning potential. And it quite possibly would have left both the Saints and Graham camps feeling more intractable in their positions, to the point where the possibility of keeping him in the black and gold for a career would have seemed like reaching for a distant star.

But now the star is staying in its orbit around New Orleans, and won’t the skies above the Crescent City look a little brighter because of it?

Sure, both sides are likely to feel a little dented by the whole process that at times looked more like a cold bank transaction than an artful deal.

To keep Graham, the Saints are forced to part with a record amount of cash for a tight end, a reported $40 million over four years with $21 million guaranteed like it’s in a Swiss bank account. It’s an interstellar leap from the $3.3 million he earned during his initial four-year deal and a hefty bump over the $7 million or so Graham would have earned as a franchise player.

To agree to remain in New Orleans, Graham will have to get past the hard negotiating line the Saints drew during the grievance hearing process, a process that saw both Saints coach Sean Payton and general manger Mickey Loomis being forced to testify why Graham is a tight end and not a wide receiver. And because he’s signing for tight end money, even record tight end money, he will probably earn about $2 million a year less than he could have gotten as a receiver.

Watching this whole story play out from the sideline, there should be no begrudging either side. It’s Loomis’ job to be fiscally responsible with player salaries to make sure the Saints have enough cash to field a team that can do more than throw to a talented tight end, even a game-changing tight end. And considering the violent nature of pro football, no one should criticize Graham for trying to grab every dollar he can. How much would it be worth to you to make your living running headlong into the equivalent of a parked car every Sunday?

But apparently both sides got past the brutal business issues to realize that they still wanted to be family. Graham recognized that maybe he wouldn’t be as productive without Payton scheming on how to get him the ball and Drew Brees throwing him those passes, and that at 27 this deal still gives him time to sign another rich contract before he retires. The Saints recognized a very promising season was likely to suffer an irreparable blow if Graham walked out the door after sulking his way through the 2014 campaign.

No, there won’t be any crossbar dunking from Graham this fall now that the NFL has banned it.

But Tuesday’s deal feels like a win-win for both sides, in a very real sense the Saints’ first win of 2014. In a tangible sense, the Saints just picked up a big forward spin of momentum going into training camp next week.

Follow Scott Rabalais on Twitter: @RabalaisAdv.