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Mr. Davis would secure consent from Mr. Waxman, then the ranking member, to issue subpoenas — a practice Mr. Waxman agreed to emulate when he took over in 2007. That system actually did lead to high-profile probes during Mr. Davis‘ tenure of the Bush administration’s handling of Hurricane Katrina, issues related to disgraced lobbyist Jack Abramoff, and the circumstances surrounding the death of former NFL player turned Army Ranger Pat Tillman in Afghanistan in 2004.

Rep. Elijah E. Cummings, Maryland Democrat and the committee’s current ranking member, sent a letter to Mr. Issa in early 2011 urging him to steer away from Mr. Burton’s unilateral style.

A committee aide, though, pointed out there was no such colloquy between Mr. Issa and former Rep. Edolphus Towns, when the New York Democrat was chairman of the committee from 2009 to 2011, and that an open line of communication between Mr. Issa and Mr. Cummings does exist.

The two have worked together on the mortgage crisis, safety issues with Toyota cars, the Secret Service prostitution scandal in Cartagena, Colombia, and the use of human growth hormone in professional football.

But Cummings staffers say that in contrast to the Davis-Waxman years, they receive little notice — or none at all — on things such as subpoenas, hearing witnesses and party staff reports.

Such complaints, the committee aide said, “are either minor or outright baseless.”

Mr. Issa, in many cases, consulted with ranking member Cummings in these instances,” the aide said.

Republicans, meanwhile, point to Mr. Waxman’s own zeal when he had the gavel and aggressively pursued issues involving the Bush administration, such as abuses by private security firms in Iraq and the use of Republican National Committee email accounts by officials in the White House.

Both inquiries resulted in congressional action, and in the latter case prompted reforms within the White House. But Mr. Davis said there was still a partisan lilt.

“The RNC had to spend over $1 million” in that case, Mr. Davis said. “It doesn’t get more partisan than that. When Obama came in, they shut down oversight.”

A Waxman staffer countered that there was aggressive oversight, but that the pursuits were always substantiated with facts.

“On investigations, Waxman’s approach was a strong believer in oversight, but his direction to us was to always lead with the facts,” the staffer said.

And even Mr. Davis conceded that politics necessarily are mixed in with the position.

“Everyone understands you’ve got a partisan job to do and a real job to do,” he said.