The Dolphins spent big Tuesday for the premier wide receiver they have so needed and also to add an unexpected prize on defense, but this franchise-in-need was doing much more than instantly improving the team. It was doing much more than just purchasing players.

The Dolphins were buying excitement.

They were nourishing the idea that maybe — just maybe — this once-proud club is turning a real corner toward better days at last.

They were buying hope.

Miami was the talk of the NFL on the first day for free-agent signings Tuesday, a free-spending, active player, and you can admit it: It felt good. It felt good and, yes, somehow different to make positive headlines. To be relevant again.

You’d say the Dolphins landing their top target, receiver Mike Wallace, was expected — except that Miami’s recent history had to make you cautious. Anxious, even.

This was the woebegone general manager, Jeff Ireland, who in the past years tried and failed to land two coveted coaches, Jim Harbaugh and Jeff Fisher, then went hard after Peyton Manning but came up short. This was the GM whose most national attention had been for asking draft prospect Dez Bryant if his mother was a prostitute. One year ago, frustration with Ireland and the Dolphins were such that fans picketed outside the club’s Davie headquarters.

Well, Ireland began his extreme makeover on Tuesday.

Funny how that happens when you have so much salary-cap money to spend that you feel like the banker in a Monopoly game.

So Miami landed Wallace, the former Steeler, for between $60 million and $65 million over five years. Crazy money? Yep. Over-spent? Maybe. You know what, though? Hope is precious commodity. It is valuable. Besides, the top free-agent a year ago, Vincent Jackson, didn’t cost much less. And Kansas City just spent almost as much to re-sign its own receiver, Dwayne Bowe.

Wallace is better than both.

He is so fast he can turn out the bedroom light and be under the covers before the room goes dark.

He might be the most game-breaking deep threat Miami has had since Irving Fryar in the mid-’90s.

Wallace means young quarterback Ryan Tannehill just got better, more dangerous.

He means fellow receivers Brian Hartline, Davone Bess (and a tight end-to-be-named) just got more open.

He means running backs Lamar Miller and Daniel Thomas just got more running room.

He means the defense just got a little more margin for error.

And he means Ireland can close a deal. Because this was the one who DIDN’T get away.

Miami also re-signed its own free agent safety, Chris Clemons, on Tuesday, and don’t lose that as significant. Clemson started all 16 games last year; he is young, solid and getting better.

Tuesday’s unexpected prize, though, was signing inside linebacker Dannell Ellerbe from the champion Ravens, which in turn allowed Miami to release pricey veteran Karlos Dansby and gain almost $4 million in spending money by doing so.

Wallace rightly will get the headlines and sound bytes but Ellerbe is a major addition, a coup. He might have been Baltimore’s best all-round defender last season. He was the young man being counted on to replace Ray Lewis (to the degree anyone could).

Now he is at the figurative and literal center of the Miami defense, a marquee-worthy guy for that side of the line of scrimmage just as Wallace is on the offense.

Add those two to the re-signing of Hartline, Clemons, defensive tackle Randy Starks and backup QB Matt Moore and Miami is off to a strong start in free agency. Work remains. Cornerback (Antoine Winfield, anyone?), offensive line and tight end remain need areas.

But when you factor the additions thus far with the blossoming promise of Tannehill and the draft bounty Miami has coming in April — including five picks in the first three rounds — hope is becoming easier. It is taking on some heft, like something tangible as much as conceptual.

The Patriots are still the Patriots, yes, but with the Jets and Bills in flux (Buffalo on Tuesday waived starting QB Ryan Fitzpatrick), Miami is clearly positioned as second best in the AFC East moving forward. The idea of an immediate end to the four-season winless streak does no seem unreasonable. The idea of an end to the 13-year drought without a playoff victory does not feel like lunacy.

The newest face of the optimism, Mike Wallace, hadn’t posted a Twitter message since March 3 as of Tuesday evening, but it was interesting to note his last Tweet. As if he sensed they might be neighbors on the Miami sporting marquee, it happened to be in praise of Heat star LeBron James. The three-word Tweet read, verbatim:

Lebron so ill.

Figure Wallace will have a chance to deliver his admiration in person now.