The housing market is showing clear signs of cooling off, and the balance of power of shifting from sellers to buyers. It’s time, then, for buyers and sellers alike to adjust their strategies.

The chill is no surprise. Higher mortgage rates leave more and more homes priced beyond the reach of more buyers.

So homes are sitting on the market longer, and in many places the average sales price is dropping. Home builders are warning about leaner times, and many of their stocks are falling.

Buyers, therefore, are in a stronger bargaining position. If you’re one of them, get tough. Chances of another buyer outbidding you aren’t as great as they were a few months ago.

Be demanding. Anxious sellers may come down on price or throw in sweeteners such as appliances or curtains. Insist on a home inspection and specify that you won’t go through with the deal if it shows needed repairs would cost more than you’re willing to pay.

Remember that sales are often contingent on the buyer receiving a mortgage at a given rate or below. When you write that into the contract, set the rate limit where you want it; you don’t need to be as accommodating as you would have had to be a few months ago. And don’t let the seller push you to a closing date that’s not to your liking – whether too soon or too late.

Also, go armed with a mortgage prequalification, which will show that you have a good chance of getting the loan you’ll need to buy the house. The buyer may meet some of your demands if there’s no doubt the sale will be completed.

As a buyer, also consider hiring your own agent, who will work for you, not the seller. Even so, when the agent recommends an offering price, ask for supporting details. What have other homes in the neighborhood sold for and how long were they on the market? Keep in mind that data from six months ago may be stale.

Sellers must be more realistic. Prices aren’t tumbling, so don’t panic. But don’t count on selling for 20 percent or 30 percent more than your neighbor did last spring.

At the same time, don’t let your agent pressure you into settling for a price that’s too low. A $10,000 cut means a lot to you. To the agent, who must split the commission with his or her boss, and perhaps with the buyer’s agent, that cut might cost only $150. The agent might be glad to settle for less to sell the house faster and move on to another deal.

Sellers also should remember that agents may be a bit hungrier and more willing to reduce commissions below the 5 percent or 6 percent they’ve been charging. Try 3 percent or 4 percent.

Sure, that gives the agent less incentive to push your house. But these days, many buyers, if not most, shop through the Multiple Listing Service, a kind of classified advertising that shows houses in hard copy and online. If a buyer wants to see your house, the agent isn’t likely to resist, even if other properties offer him higher commissions.

Also, look carefully at the contract you sign with an agent. If the agent wants a six-month deal, think about insisting on only three, so you can get someone else if you’re not happy.

Remember: Just about every aspect of your deals with the agent and homeowner are negotiable, so don’t assume anything is standard.