The Taylor Wessing survey of individuals involved in corporate restructures found 61% believed they should look at the level of return to a scheme, and 44% stated it was the profile of the employer.
Where the Pension Protection Fund (PPF) considers a potential restructure - such as a regulated apportionment arrangement (RAA) - insolvency again ranked top, with 89% stating it was the lifeboat fund's most important factor.
The survey of actuaries, trustees, and insolvency practitioners also found 66% believed the level of return was important when the PPF considered such a proposal, while 44% felt it was the level of return to other creditors.
Conversely, the law firm's Pensions in Restructuring Survey 2017 found that just 5% felt whether properly-advised trustees had agreed to the proposal was important to the PPF.
Taylor Wessing partner Mark Smith said the rigidness of the immediate insolvency rule, which is one of a number of factors considered in TPR and PPF's tests for RAAs, had meant some appropriate deals had not been allowed.
"In my experience, the regulator and the PPF have been using that particular factor as a gateway, saying they're not going to engage in any meaningful discussions about these proposals because they don't think they've satisfied that hurdle," he said.
"That's been very much at the fore in discussions. Although it's absolutely right we don't have a system where people can just free themselves from pension liabilities when the pension becomes inconvenient for them, the strict approach has scuppered a number of dealt which, on the face of it, could and should have been valid deals.
"There's something to be said for a bit more flexibility in it. That would be helpful to make things work a bit better, rather than sometimes forcing insolvency with no pensions deal when viable business perhaps could have been saved."
The survey found that over half (58%) had seen an increase in the number of employers seeking a restructure proposals over the past year, with just 5% seeing a decrease.
Yet, the regulator and the PPF are no more likely or less likely to agree to such deals, over two-thirds (69%) said.
Smith said these results may have been driven by parliamentary action over the past year, as well as high-profile cases including BHS, Hoover, and Tata Steel.
"It is quite a buoyant market for this kind of activity," he continued. "We've had the focus on it from the government over the last year, including the select committee, the [Department for Work and Pensions'] green paper and Theresa May's statements."
When asked which view was closest to their own on the extent of the regulator's powers, over a quarter (27%) said the regulator should be given more powers to require clearance to be mandatory in certain mergers and acquisitions.
None said there should fixed fines where TPR uses its moral hazard powers, while 11% said the watchdog's current powers are fine as they are.