For years bankers have had only modest success getting customers to drop paper statements, so some are introducing accounts that are managed almost exclusively online and do not offer them at all.

Bankers say most customers continue to receive paper statements out of habit, and that the only way to change these habits may be to impose, and enforce, a no-statement policy.

Bobby Berman, the group executive vice president of e-commerce and research strategy at Frost National Bank in San Antonio, a unit of Cullen/Frost Bankers Inc., said few people really need a paper statement, and that given the right encouragement, customers would be willing to consider viewing them online instead.

"I think you've got a bunch of people who just don't care, who say, 'I don't look at my statement, but I don't want to take the time to turn it off,' " Mr. Berman said. "I think it's more of an inertia."

The trick has been to find an effective way to push the idea. Frost's past attempts to encourage switching from paper to online statements have not done very well, Mr. Berman said.

"We've tried an incentive-based approach where we actually … paid them some money to do it," he said. "We got a little bit of lift from that. It wasn't great."

Frost National has also tried to position online statements as a security feature and a convenience, Mr. Berman said. "You have fewer hands touching the mail, so there's less aptitude for fraud. You don't need to save them, because we have eight years of history online."

"We've continually tried different messages," but only 10% to 20% of the bank's accounts do not use paper statements.

But with the Momentum account Frost rolled out last week, the bank does not have to encourage customers to choose online statements — it is the only option. Mr. Berman said there have been no problems so far with the absence of statements. And if anyone demands one, they would have to switch to a different account. "We are definitely going to hold the line on this," he said.

PNC Financial Services Group Inc. is following a similar strategy with its Virtual Wallet account, which was introduced last month and also eschews paper.

Thomas S. Kunz, PNC's head of payments and e-business, said customers who bank online are more receptive to viewing statements on the Web site. Roughly 17% of PNC's customers have turned off paper statements, but of customers PNC considers active online banking users (those who go online at least once every 90 days), 40% have done so, he said.

He said that people who bank online typically "don't reconcile or balance the way some other segments had to, because they write a lot less checks."

"Inertia and the attachment to the statement, the piece of paper, is the biggest hurdle for" banks trying to switch customers to online statements.

To convince some of the Pittsburgh company's customers to shut off paper, PNC had to make the online statement as close to the paper statement as possible: it is presented as a pdf file which, when printed, looks exactly as it would appear in the mail, he said.

Both bankers said that eliminating paper statements can generate significant savings. Mr. Berman put the figure at about $5 to $7 per account, per year. "The benefits for us are pretty obvious," he said.

Cindy Reeves, Frost's compliance manager, said banks are required under the Federal Reserve Board's Regulation E to provide a monthly statement for all consumer accounts that have electronic transactions (or quarterly for those without). Statements can be provided online as long as the enrollment process complies with the Electronic Signatures in Global and National Commerce Act.

Many banks encourage people to drop paper statements, and some are starting to gently nudge them in this direction, though few have eliminated the option.

Since October, Citigroup Inc. has made paperless statements the default for customers who sign up for checking, savings, and money market accounts online; it plans to do the same for branch enrollments next year.

However, Marylou Dowd, the executive director of customer experience for Citibank online, said paper is still an option. "We would never make it mandatory for a customer to enroll in paperless," she said.

For those signed up for paperless statement delivery as part of their online application, "they have the option to unenroll," but very few do so, Ms. Dowd said.

ING Bank FSB, the U.S. unit of ING Group NV of Amsterdam, has a paperless checking account where customers get neither checks nor paper statements.

Lance Ellisor, the director of product management for Fiserv Inc.'s digital document unit Epsiia in Austin, said a handful of his company's 400 bank and credit union customers either have accounts that do not offer paper statements or that use online statements as the default preference, though he would not name any.

And though he said that some banks have used the green message successfully to get people to switch, "where success is really going to happen is (a) for folks who force the issue by forcing the choice, and (b) when they make it really easy for their users to control their data" online.

James Van Dyke, the principal and founder of Javelin Strategy and Research in Pleasanton, Calif., said banks can do a better job of encouraging customers to turn off paper without eliminating the option entirely.

"In general, I think banks' efforts to get consumers to turn off paper statements" have been "mediocre in terms of effectiveness," he said.

Banks have been using messages about environmentalism and security, but customers' top concern is reducing clutter, Mr. Van Dyke said. "Bankers are only anecdotally considering consumers' preferences."

Because so few customers have switched to online statements, banks must continue to support the machinery to produce paper ones, and they have not been able to realize the potential savings from eliminating paper statements, he said. "They don't get much of the savings until they shut down one of those pieces of redundant equipment."