It is getting easier for some buyers to land a house with less money up front.

More lenders are lowering down-payment requirements, allowing borrowers to commit 3%—or even less—of a home’s purchase price to get a mortgage. Many had been requiring down payments of at least 20% since the recession began.

Some lenders also are waiving mortgage-related fees, and more are allowing down payments to be made by other parties, such as the borrower’s family.

The deals are aimed at buyers with good credit scores and a steady income who have been unable to save enough for a sizable down payment. They are often targeted at buyers who live in expensive housing markets, where even a small down payment can equal tens of thousands of dollars.

Low-down-payment mortgages have long been available. The Federal Housing Administration insures mortgages with down payments as low as 3.5% and it is lowering the annual mortgage-insurance premiums on new mortgages beginning on Monday.

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The trend has picked up since mortgage-finance giants Fannie Mae FNMA, +2.51% and Freddie Mac FMCC, +1.84% , which buy most mortgages from lenders, recently lowered the minimum down payments they will accept to 3% from 5%. The changes are driven by an Obama administration effort to make homeownership affordable to a wider group of buyers.

Borrowers should be aware that small down payments leave them more at risk of owing more on their mortgage than the property is worth should home values in their market decline, says Jack McCabe, an independent housing analyst in Deerfield Beach, Fla.

In addition, borrowers likely will incur higher costs over the life of the loan, including higher interest rates and, often, mortgage insurance.

The moves come as mortgage originations declined substantially last year. Lenders gave out an estimated $1.12 trillion in mortgages in 2014, down 39% from a year earlier and the lowest amount since 1997, according to the Mortgage Bankers Association, a Washington-based trade group.

Most mortgages have been going to existing homeowners who are refinancing into lower interest rates, as demand among home buyers has been low compared with historical norms.

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Regions Bank, a unit of Regions Financial RF, -0.99% , launched a mortgage program in September that allows some borrowers to make a 5% down payment. The bank says it will lower that requirement in the next few weeks to 3%. Borrowers must not have owned a property or had a mortgage in the past three years, among other requirements.

TD Bank, the U.S. unit of Toronto-Dominion Bank TD, -0.72% , is allowing first-time buyers to put as little as 3% down through its “Right Step” loan program. The bank—which also is extending the offer to low- and moderate-income borrowers as well as those purchasing a home in some up-and-coming neighborhoods—lowered its cash-down requirement from 5% last year.

The banks allow borrowers’ down payments to be partially or fully funded by family, nonprofits or other sources.

Lenders also have been lowering the bar for larger mortgages, known as “jumbos,” which they typically hold on their books. Such loans exceed $417,000 in most parts of the country and $625,500 in pricier housing markets such as New York and San Francisco.

In November, PNC Financial Services Group PNC, -0.10% began allowing exceptions to its down-payment requirements for jumbos, says Tyler Case, a loan officer at PNC’s Fords, N.J., branch. The lender, which has been requiring at least 20% down for jumbos up to $1.5 million, lowered that to 15% for borrowers whose income and assets go beyond what the bank generally requires.

To qualify, borrowers will need a higher credit score and less debt relative to their income than is usually required, as well as having savings after the home purchase equal to at least 12 months of mortgage payments.

PNC also is offering exceptions on down-payment amounts for larger loans up to $3 million.

Wells Fargo WFC, +0.08% , meanwhile, began permitting down payments of as little as 10.1% last year on jumbo mortgages. Previously, its lowest down payment on jumbos was 15%.

Borrowers who want to get a mortgage with a particular lender could ask if it would allow a lower down payment than what is officially offered.

PNC, for example, isn’t advertising its 15% option, Mr. Case says. Instead, it is offering it to eligible borrowers who inquire or mention that they have been offered lower down-payment loans at competitors, he says.

The costs associated with these low-down-payment mortgages can vary significantly. The interest rate and fees borrowers pay often depends on whether the lender plans to sell their mortgage to Fannie or Freddie, or if it plans to hold the loan on its books, in addition to borrowers’ qualifications.

Borrowers need to compare costs, including the interest rate, whether they have to pay any upfront fees to get that rate, and what their total costs to get the loan will be. A lower interest rate might not be a good deal if it requires larger out-of-pocket payments.

Often, borrowers have to pay an extra fee for private mortgage insurance, which protects the lender from incurring significant losses if the borrower defaults, in exchange for a low down payment. In most cases, the fee is included in the monthly mortgage payment, though borrowers sometimes have the option to pay it as an upfront charge.

Mortgages purchased by Fannie Mae and Freddie Mac usually require private mortgage insurance if the down payment is less than 20%. Lenders generally decide which mortgage-insurance firm to work with.

Borrowers with higher credit scores, smaller loan amounts and fixed-rate mortgages pay less.

The size of the down payment also matters. Typically, someone with a FICO credit score of 760 or more—on a scale that tops out at 850—who is making a down payment of just under 5% and getting a $400,000, 30-year fixed-rate mortgage will incur at least a 0.57% fee, according to Radian Guaranty, a unit of Radian Group, and Mortgage Guaranty Insurance, a unit of MGIC Investment, two of the largest private mortgage insurers.

That comes out to $190 a month. The same borrower with a down payment of just under 10% would incur a fee of at least 0.43%, or $143 a month.

Before signing up, borrowers should find out if they will incur these costs, and for how long. They should consider asking their lender if they can stop paying this fee when they reach at least a 20% equity stake in the home through a mix of home-price appreciation and amortization, for example, says Keith Gumbinger, vice president at mortgage-information website HSH.com.

Lenders who hold low-down-payment mortgages on their books typically don’t require this insurance. But the loans may not be a bargain, he says, because they often charge interest rates that can be an eighth to a quarter of a percentage point higher.