The venerable U.S. Savings Bond, a Christmas stocking stuffer for grandchildren for more than 60 years, has recently become a hot item. Investors looking for a risk-free way to earn more than the 1.2 percent available on three- and six-month Treasury bills -- and more than what bank certificates of deposit are paying -- have leapt on the bonds for short-term savings. Some savings bonds are yielding as much as 4.08 percent.

Last week the Treasury Department, pointing out that the bonds "are designed to be a long-term savings vehicle," doubled the minimum holding period to one year, effective with bonds sold in February.

But that is only one of the challenges facing Treasury and its Bureau of the Public Debt in running the program that has put the familiar pieces of paper in the hands of about 55 million people. Operating the program is so expensive relative to the amount of money raised that some members of Congress have questioned whether the government should continue to sell the bonds. And the department's appropriation bill for this year, which is pending in the House, would eliminate $22.4 million requested by the Bush administration to cover advertising and other marketing costs in the current fiscal year.

Treasury officials readily acknowledge that the savings-bond program is expensive to administer. But they want to continue it for investors who are seeking a secure investment but who may have only the minimum $25 to buy a single bond, or a few hundred dollars, but not the $1,000 minimum for a Treasury bill or note. The Treasury's goal, one official said, is to reduce the program's cost by eliminating the sale of paper bonds -- now available through about 40,000 financial institutions -- and going entirely electronic, perhaps in two to three years. Within a few weeks, Treasury plans to make it easier to buy bonds using the Internet.

The cost problem is this: The vast majority of U.S. Savings Bond owners, many of whom are children who received them as gifts, hold only a few bonds, and in small denominations. Collectively the bonds represent only about $190 billion, or 3 percent, of the $3.4 trillion worth of government debt owned by the public.

Aside from being suddenly popular with savvy investors searching for higher short-term yields, savings bonds remain very popular with small investors. That popularity is enhanced by the fact that they can be bought from Treasury Online using a credit card, which has added to the "churning" of the bonds, because some of the cards give the purchasers frequent-flier miles to boot.

But the bonds themselves are attractive. A Series EE bond, which is sold at 50 percent of its face value in denominations ranging from $50 to $10,000, increases in value each month according to an interest rate equal to 90 percent of the six-month average of five-year Treasury notes. It currently yields 3.25 percent.

The Series I bond, issued in the same denominations, is purchased at face value and pays an interest rate that is a combination of a fixed rate and a semiannual inflation rate tied to the consumer price index. This is the bond currently yielding 4.08 percent. Furthermore, a bondholder can defer federal income taxes on the bonds' appreciation until they are redeemed or they mature. The interest is exempt from state and local income taxes.

Administering savings bonds' small slice of the national debt requires the equivalent of 1,020 full-time employees at the Bureau of the Public Debt, nearly three-fourths of all its workers. The Bush administration sought about $200 million to run the bureau in the current fiscal year, with about $150 million for savings bonds. The other $50 million was all that was needed to sell and redeem the other $3.2 trillion worth of debt, all of which is auctioned electronically and most of which is purchased by larger financial services firms for themselves and their clients.

Rep. Ernest J. Istook Jr. (R-Okla.), chairman of the House Appropriations subcommittee responsible for Treasury's budget, last year led an effort to eliminate money for marketing savings bonds. That could cut the jobs of many of the 140 bureau employees working on marketing bonds, and the National Treasury Employees Union has begun an effort to persuade Congress and Treasury to continue the marketing and to preserve the use of paper bond certificates.

"The overhead costs are exorbitant right now," Istook said in an interview. "It costs 53 times more to borrow through savings bonds than through the sale of marketable Treasury securities, and that cost is borne by the taxpayers.

"It's like buying groceries. If you buy small quantities, you pay more than if you buy more than the giant economy size. If you are losing money on each transaction, it does not make sense to advertise for more transactions.

"We also wanted to get Treasury to acknowledge the problem so they can help us find the answer."

Peter R. Fisher, Treasury undersecretary for domestic finance, has already initiated several changes in the way auctions of Treasury bills and notes are conducted, all with the goal of making them more competitive so as to minimize the interest rates the government pays when it borrows money.

As Fisher explained in several speeches, "the objective over time is to borrow at the lowest cost."

In that vein, Fisher announced in 2001 that no more regular 30-year Treasury bonds would be sold because it has consistently cost less to issue 10-year notes than the bonds. Other smaller steps, such as making it much easier for large investment firms to place competitive bids for securities directly rather than through bond dealers, were designed to increase the number of bidders so Treasury could pay lower rates.

In the mid-1980s, Treasury stopped issuing all paper certificates as evidence of ownership of its marketable securities. Now even small investors place noncompetitive bids through the Treasury Direct system. And that is now the direction in which the savings-bond program is headed.

Within a few weeks, Treasury will begin selling savings bonds that will be all electronic; that is, they will be purchased through a Bureau of the Public Debt Web site and will be in the form of an entry in an electronic database. For those purchases, no paper bond will be issued, a Treasury official said.

Then there will be a transition period of two or three years in which financial institutions will stop selling savings bonds and providing paper certificates. That, however, would still leave millions of paper bonds outstanding, which would still be costly to service.

Istook agrees that the government has no choice but to incur those costs. But stopping issuing paper is just "common sense," he said. "You don't want to dig the hole any deeper."

As savings bonds are cashed in, the amount of paper outstanding will shrink -- but not necessarily rapidly, since most of the bonds have a 30-year maturity and in some cases can be exchanged at maturity for other bonds lasting an additional 20 years.

If Treasury does get to the point that no more paper certificates are issued, the department will try to figure out what incentives it might offer to get bond owners to exchange their certificates for an electronic entry.

"We need to be creative and induce people to convert to electronic funds," the official said.