WASHINGTON — Executives from insurance firms Prudential Financial and Country Financial said Thursday that the Financial Stability Oversight Council should be more transparent with its regulation despite recent reforms.

The Senate Banking Committee's subcommittee on securities, insurance and investment hosted a hearing with the insurers and an academic to discuss the FSOC's designation and oversight of systemically important nonbanks.

Although FSOC has made efforts recently to further open its process to companies and the public, those representing the insurance industry said they didn't go far enough.

"I believe the FSOC has an obligation to provide a roadmap of whatever combination of criteria are necessary to de-risk an institution on a U.S. systemic basis," said Robert Falzon, executive vice president and chief financial officer at Prudential, who testified on behalf of the American Council of Life Insurers and the American Insurance Association.

The FSOC designated Prudential as a "systemically important financial institution" in 2013. The insurer tried to appeal the decision with regulators, but ultimately lost that battle. Critics of the process have argued that companies are not given enough information to explain regulators' decision, making it difficult to know how they might be able to change their business to remove concerns about systemic importance.

"Lacking the justification for the on-ramp, we lack the tools to define the off-ramp," Falzon said.

Kurt Bock, chief executive of Country, which has not been designated as systemically important, added that he worries about whether regulators look too closely at the size of a company, as opposed to other factors — such as interconnectedness and concentration — that determine risk to the system.

"It appears size is a part of the designation, not necessarily activities," said Bock, who represented the National Association of Mutual Insurance Companies and the Property Casualty Insurers Association of America.

He added: "To know the why and the how is always important to us, and we do a good job of managing when we know why — which I believe is one of the issues in terms of the lack of transparency of the process."

Lawmakers, meanwhile, highlighted similar concerns, noting that companies should be given a chance to understand FSOC designations and even remove the SIFI label if certain company risks are mitigated.

"I am interested in finding bipartisan solutions to ensure that FSOC is more transparent during the designation process about which activities, together or separately, pose the greatest risk from a company so that they can be addressed," said Sen. Mike Crapo, R-Idaho, chairman of the subcommittee, in his opening statement.

Sen. Mark Warner, D-Va., the top Democrat on the subcommittee, reiterated that he also worried about SIFI designation becoming a "Hotel California" where "once you check in, you can never check out."

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