It had been more than five months since the Saints finished the 2013 regular season having permitted the fourth-fewest yards and points on defense while amassing the fourth-most yards on offense. It had been that long since the Saints allowed the second-fewest passing yards on defense while passing for the second-most yards.

Yet strong traces of that symmetry persisted at the Saints’ three-day minicamp last week in Metairie. Whether it was the first-team offense or the “1s” on defense, one side frequently got the upper hand — and then the other seized the momentum right back.

Some of the minicamp’s final moments Thursday vividly illustrated that. With temperatures hotter than they had been all minicamp and players undoubtedly fatigued, the atmosphere at the Saints practice facility was relatively muted — until veteran receiver Robert Meachem roared past third-year defensive back Corey White and caught a line-drive throw toward the middle of the field from quarterback Drew Brees for a long gain during a 7-on-7 drill.

The play drew the heartiest “oohs,” “ahhs” and claps till that point.

But then, in 11-on-11, Brees sought out Meachem again. Meachem’s body was facing the ball, and he was poised to haul the throw in — until cornerback Keenan Lewis reached an arm around the receiver and emphatically swatted it to the ground, prompting louder “oohs,” “ahhs” and applause.

It was even louder when safety Kenny Vaccaro intercepted Brees on the first snap of 11-on-11. But the loudest came last, when Brees directed a 13-play, 70-yard, two-minute-drill drive that culminated in a touchdown pass to receiver Kenny Stills on third-and-goal from the 4.

Throughout minicamp, the Saints tried to minimize big plays and miscues because drills featured neither contact nor equipment beyond helmets. Perhaps the most-uttered phrase was, “Things will be different when pads come on” and contact is live during training camp and the preseason, let alone in Week 1 at Atlanta.

The offense did without rookie receiver/first-round pick Brandin Cooks (finishing up his junior year at Oregon State) and All-Pro tight end Jimmy Graham (contract dispute). The defense did not have marquee free-agent addition Jairus Byrd, the three-time Pro Bowl safety sidelined while recovering from what has been described as minor back surgery.

But after his touchdown in the two-minute drill, Stills said, “It’s important we can execute that way this time of year.”

That’s certainly true. It’s still the offseason, but it has to be encouraging to coach Sean Payton that both his offense and defense were able to operate so well so early against opponents who were some of the NFL’s most successful last year.

Kicking game’s on target

But there’s another phase of football beyond offense and defense. A significant portion of it is punting and field goals, and both elements were off to solid starts at minicamp.

On Thursday, incumbent kicker Shayne Graham and challenger Derek Dimke each were perfect on tries from 33, 37 and 39 yards, an indication that the competition may be compelling at training camp.

Thomas Morstead nailed multiple punts that were downed by the goal line or would have forced fair catches between the receiving team’s 10 and 20. Morstead said he felt he “left some meat on the bone in that area” last season, and it’s a point of emphasis for his upcoming campaign.

Earlier in minicamp, Morstead boomed punts that hung high and occasionally had enough power on them that players had to step back to field them.

That’s not surprising: In 2012, Morstead set franchise records for gross punting average (50.1 yards) and net punting average (43.2).

But Morstead said he’s in better physical shape heading into 2014 than he was preparing for ’13, when he was recovering from left knee surgery.

“I wasn’t able to train my body the way I wanted to last year,” said Morstead, who’s right-footed. “I feel very, very good so far.”

On Jimmy

The grievance hearing stemming from the franchise tag battle between Graham and the Saints is scheduled for Tuesday and Wednesday.

To prevent Graham from becoming the most-sought unrestricted free agent when his contract expired in March, the Saints handed him a one-year franchise tag worth about $7 million that classified him as a tight end — the position at which he was drafted, at which he has been selected for two Pro Bowls and which he lists on his Twitter bio.

Since he spent most of his time in 2013 lining up out wide for the Saints while leading them with 1,215 receiving yards and the NFL with 16 touchdown grabs, Graham is arguing that he deserves a franchise tag that considers him a wide receiver — and is worth about $5 million more.

The franchise tag would be irrelevant if the Saints and Graham hammer out a long-term deal.

But any ruling on whether Graham should be considered a receiver or a tight end for franchise tag purposes would affect negotiations.

Everyone has an opinion on this. Here’s mine.

Half of the 22 touchdowns Brees threw from inside the opposing 20 in 2013 went to the 6-foot-7, 260-pound Graham, clearly demonstrating his value as a target near the opponent’s goal line.

After one season of college football and four years in New Orleans, Graham’s 41 touchdown catches are fourth all-time for the Saints and the most among the club’s tight ends.

His 301 catches and 3,863 receiving yards rank sixth and seventh all time for the Saints, and they each are tops among tight ends who have suited up for the franchise.

He holds single-season team records for catches (99 in 2011) and receiving touchdowns (16 last season).

He helped the Saints to the playoffs in 2010, ’11 and ’13.

Though the franchise won its only Super Bowl the year before Graham arrived, it’s absolutely worthwhile for the Saints to make him the NFL’s best-paid tight end ever by giving him more than New England’s Rob Gronkowski’s $9 million per year — even if it’s up to $2 million more annually.

But giving Graham franchise receiver money each year is tough to justify.

He does not line up at wideout every play — true franchise receivers do that.

Therefore, Graham is not defended like wideouts are on every snap — and true franchise receivers are.