Shopping for a mortgage for a new home or a refinancing? The standard 30-year, fixed-rate mortgage may turn out to be the best deal going if you plan to own your home for a long time, since you can lock in today at near 40-year lows.

But if you expect to move or pay off your loan within a few years, consider a “hybrid” mortgage. Some of these are very attractive right now, thanks to the Federal Reserve’s string of interest-rate cuts.

Hybrids are easily overlooked, and many borrowers don’t understand them. But they’re actually quite simple: The interest rate is fixed for an initial period of three, five, seven or 10 years; after that it, “adjusts” every year.

That’s why it’s a hybrid — it combines the features of a fixed-rate mortgage with those of the more common one-year adjustable-rate mortgage, which goes to a new rate every year, starting 12 months after the loan is taken out.

Typically, the starting rate on ARMs is considerably lower than you’d get on a standard mortgage, though you risk future hikes.

The average “3/1” adjustable-rate mortgage recently charged just 3.74 percent for the first three years, according to HSH Associates, the Butler, N.J., tracking firm. The average for a 30-year fixed mortgage is around 5.5 percent.

So for every $1,000 you borrow, the average 3/1 ARM will save you $1.05 a month. That’s $210 a month on a $200,000 mortgage — about $7,500 over the three years before the first adjustment.

And it can be even better. If you’re willing to pay 2 “points” — an upfront fee of 2 percent of the loan amount — you can start with a rate below 3 percent.

The average 5/1 ARM charges only 4.25 percent for the first five years, the 7/1 ARM goes for 4.64 percent, and the 10/1 ARM charges 4.98 percent.

There is, of course, that all-important catch: After the initial period, you’re at the mercy of the marketplace. Most ARM adjustments are figured by adding 2.75 percentage points to the rate paid by one-year U.S. Treasury note at the time of the adjustment. Today, that’s about 1 percent.

Most 3/1 ARMs work the same as one-year ARMs. The rate can go up or down no more than 2 percentage points annually after the first three years, for a total of no more than 6 points over the life of the loan.

Most five-, seven- and 10-year ARMs are limited to a five-point change on the first adjustment, no more than two points each year after that and no more than five points total over their lifetimes.

The 7/1 and 10/1 ARMs aren’t very good deals right now, as their initial rates aren’t much lower than you’d get on a 30-year loan.

But the three- and five-year hybrids can be good for homeowners who expect to sell or pay their loans off before the first rate adjustment. That way, you get the substantial upfront savings without the risk of going to a 9 percent or 10 percent rate later.

Of course, you could get a hybrid and hope to refinance as the initial term expires. But by then, prevailing rates may be much higher than they are today, so your new rate might well wipe out all the savings you’d enjoyed in the initial years.

By getting a lower rate and lower monthly payments than you would with a 30- or 15-year loan, you can break even more quickly on refinancing costs such as title insurance and the appraisal fee.

And since you’ll have a lower monthly payment, you can make extra payments on your loan to retire it early. That can save you many thousands during the years you have the loan.

Hybrid mortgages aren’t advertised as widely as the fixed loans and one-year ARMs, but there are plenty of them out there. You can track them down by calling mortgage lenders.

Or look at the online listings of Bankrate.com: www.bankrate.com.

To see what your payments would be, use the HSH Associates calculators at www.hsh.com.