Can a pay cut be pareto improving?

Although I greatly enjoy the competitive balance that the NHL salary cap has created in hockey, it seems to me there is one glaring inefficiency. By limiting the amount of money teams can spend, mediocre players with high salaries who would have a job in the NHL based on merit are instead sent to the minor leagues because given the cap, their salary allocation can best be spent elsewhere.

Several overpaid players have been shipped to the American Hockey League this season so their massive salaries don't count against the salary cap: Wade Redden ($6.5 million), Sheldon Souray ($5.4 million), Michael Nylander ($5.0 million) and Jeff Finger ($3.5 million). The NHL club still has to pay their salary, but it doesn't count against the salary cap.

So while these players take home massive pay cheques, it's a dead-end career-wise. Playing in the NHL is clearly utility improving for most players, with players frequently accepting lower salaries for a shot at playing in the NHL (my favourite example is Sergei Shirokov). Many players will also sign contracts for less money than they could earn elsewhere if it means they have a good shot at winning the Stanley Cup. And playing in the minors isn't a good way to impress NHL teams and convince them to pay you well when your current contract expires and you need a new one. So while the big pay cheques are nice in the short term, they clearly aren't the be-all-end-all for most players.

For many of the high-paid players toiling in the minors, if they were paid at lower salaries ($1 million, for example), they'd immediately have teams chomping at the bit to add them to their NHL rosters. Thus, I wonder why we don't see players, at the margin, negotiate pay cuts mid-contract in order to stay in the NHL. For some players, such as Wade Redden, the multi-million-dollar pay cut he'd have to take to stick around probably wouldn't be worth it. But for someone like Brad Lukowich, whose talent was probably good enough for the Vancouver Canucks last season had his $1.6-million contract not been so rich, wouldn't it have made sense for him to take a pay cut of a few hundred thousand dollars so he could have spent the whole season in the NHL, instead of toiling much of it away in the minors?

In economics, we call this a pareto improvement: either the team or the player could become better off, with neither become worse off. In layman's terms, this is a win-win situation. So why don't we see some players and teams mutually agreeing to cut players' salaries if it makes the difference between staying in the NHL and getting sent to the minors?