The rules are filled with odd contradictions. Lobbyists themselves are not allowed to pay for trips, but their corporate clients can. And lobbyists are permitted to give huge sums to nonprofit groups that can sponsor travel. They can also travel to destinations and meet the lawmakers once they get there, though they cannot go on the same plane.

Seizing on the loopholes, lobbyists and the companies that employ them are still underwriting trips by dozens of members of Congress, particularly those in the House, the Times review shows. The companies finance much of this travel indirectly, getting around the spirit of the rules by giving money to nonprofits, some of which seem to exist largely to sponsor trips. In fact, the rules may have had the unexpected effect of obscuring who is actually paying for a lawmaker’s junket.

“If a nonprofit group is essentially just being used as a pass-through entity for corporate players that otherwise could not sponsor an event, that is a fraud and that is not allowed,” said Representative Zoe Lofgren, the California Democrat who leads the House ethics committee.

The rules have had some real impact. Privately financed travel for members of the House has dropped to fewer than 400 trips in the first 10 months of this year, compared with 1,100 in the same period in 2005. The drop in Senate travel has been even greater: Senators took just 24 trips in the first 10 months of this year, compared with 189 in the same period in 2005. Democrats and Republicans traveled proportionate to their numbers in Congress.

The universe of regular sponsors has been reduced to fewer than a dozen big foundations and associations, the Times analysis shows. Many of the trips are sponsored by organizations with ideological and policy agendas, rather than commercial interests. Most of those rely, at least in part, on corporate financing to underwrite trips for lawmakers.

Their internal policies vary widely in how they seek to insulate the trips from corporate influence. The Aspen Institute, for instance, tries to block corporate influence-peddling by barring lobbyists from its events and declining corporate contributions for the trips, a spokesman said.

But not all groups are as strict. Some nonprofits take money from major corporations with lobbyists, like Lockheed Martin, the defense contractor, Eli Lilly, the drug company, and Volkswagen, the automaker, to sponsor events for lawmakers during the trips.