So there they sat for two hours last February at O'Hare Airport near Chicago, swapping tales of punts and kickoff returns while waiting for the flight taking them to the Ed Block Memorial Courage Award ceremony in Baltimore.
Steve Tasker, the Bills No. 1 kid on the block, and Mike Westhoff, the Miami Dolphins special teams coach.
"We spent a lot of time together the next few days. Steve was on Plan B and I really tried to get him to come to Miami," said the coach.
"He never said no. But I knew he liked Buffalo and I knew it would be hard to get him out of there."
As it turned out, though Westhoff lobbied hard, the Dolphins never made an offer.
"You might say we didn't jump on the Tasker bandwagon. But if there was one vote for going after him, it was me," Westhoff said. His (Westhoff's) disappointment is heavier now than it was last spring.
With two blocked kicks, two recovered fumbles, one forced fumble, a few special teams minor miracles and a Pro Bowl berth, Tasker is a lot on the Dolphins' minds.
And the uglier the weather turns this week, the more prominent he will become.
When it's cold, wet and hard to run, offenses slow down, defenses take hold and special teams have a way of being the difference in the game.
Miami coach Don Shula has known that at least since that snowbound day in Foxboro, Mass., on Dec. 12, 1982, when some guy in a snow plow cleared
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Tasker: All-Pro has it down to a science
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a spot for the field goal which beat the Dolphins, 3-0.
Lost somewhere in all the banter this week about Miami's defense vs. Thurman Thomas or Dan Marino vs. the Bills' secondary is the fact that these may be the best two special teams in the National Football League.
In this corner, the Bills, who have blocked six kicks, turned around the Los Angeles Raiders and Denver games and haven't allowed a punt return of more than 21 yards or a kickoff return of more than 30.
In the other corner, the Dolphins, who haven't allowed a block, whose field-goal kicker, Pete Stoyanovich, is 21 for 23 with only one miss (44 yards) inside the 50, and who haven't allowed a punt return of more than 36 yards or a kickoff of more than 38.
"Well, they are and they aren't the best," said Westhoff. "Without Tasker, to tell you the truth, they would still be good, but measurably less than they are with him. Steve Tasker is just an outstanding player, and you can't underestimate what he can do to a football game."
It wasn't just Tasker's blocked punts against the Raiders and Philadelphia which sent Westhoff scurrying for superlatives.
"The thing you're impressed with is that he was the only guy rushing the kicker."
Reserve cornerback Kerry Glenn, who might be the Dolphins best special-teams player this year, says Tasker "comes off the corner better than anyone in the league. The guy has it down to a science and we just have to contain him."
He may be a blur off the corner, but Tasker will line up anywhere, and the job of adjusting the blocking schemes will fall to special teams captain Jim Jensen.
"You have to be aware of him. He's a big-play guy. We know that. But we have a lot of confidence in what we're doing," said Jensen.
Glenn will "lock on" with Tasker in some one-on-one situations.
"Kerry wants to do it and he's taking this as a real challenge," said Westhoff. "He (Glenn) might have (Tasker) on a particular return. I just believe you put your top people on their top people. You get the best out of them that way."
Get Westhoff wound up and he'll go through the entire array of Buffalo special teams work.
"They don't do anything exotic. In fact, their schemes are a lot like ours," he said. "But they've got eight guys on some of their units who have been together for years. That's a big plus. Scott Norwood doesn't hit the end zone with consistency, but he pins you in the corner down inside the 10 and it's tough to break a return."
But always the discussion gets back to Tasker.
"Some people think he's a one-dimensional guy," said Westhoff. "Count the number of plays he's in on, and how he affects a game. He makes their special teams."