(MONEY Magazine) – Ever since the summer, when hurricanes Andrew and Iniki caused more than $9 billion in damage, some storm victims in South Florida, Louisiana and Kauai have complained about the sluggishness of insurers in handling claims. That fact may lead you to ponder this: Just how responsive would your carrier be if you had to file a claim? The answer is more encouraging than you might expect. To find out how well the nation's 3,900 homeowners insurers treat their 60 million customers, MONEY interviewed state regulators, consumer advocates and industry officials. Our conclusion: Most companies are remarkably diligent in meeting their obligations. ''On a day-to-day basis, there generally aren't many complaints about homeowners insurers,'' says John Richards, insurance commissioner in South Carolina, where Hurricane Hugo did an estimated $4.2 billion of damage in 1989. Two insurers with high consumer-satisfication levels, according to complaint studies by state insurance departments: State Farm and United Services Automobile Association. Two with higher than average complaint records in more than one state: Colonial Penn and Metropolitan Property & Casualty. Both insurers say the gripes are because they have not renewed some policies owing to a change in business strategy. In yet another case of an insurer taking flak, California Insurance Commissioner John Garamendi in September said Allstate and eight of its agents failed to handle their 1991 Oakland fire claims ''within a reasonable time.'' An Allstate spokesman says the company is dedicated to ''resolving the issues as quickly as possible.'' A January 1993 hearing will determine if Allstate must stop offering new policies in California for up to a year. The most common disputes, however, result from homeowners' ignorance about what their policies cover. ''Most people don't read their contracts until after a loss,'' notes Wayne Cotter of the New York State Insurance Department. Consumer advocates add that agents should explain their policies' limitations more clearly. Here are three ways you can avoid conflicts with your homeowners insurer: -- Choose a company with a superior record of serving its policyholders. To do this, write to your state insurance department and ask to compare the number of complaints against the company you're considering with that for similar- size insurers. -- Read the policy's fine print to find out precisely what is covered. For instance, even the best standard policy -- the so-called HO-3 -- won't cover damage from floods or earthquakes. You must pay about $300 to $700 extra a year for that. -- Buy guaranteed replacement-cost coverage. Some homeowners with losses become livid when their insurers pay, say, only $1,000 to replace damaged carpeting that had been bought for $5,000. They don't realize that they own actual-cash-value policies, which pay the replacement cost of an item minus its depreciated value. If you pay 10% to 15% more for guaranteed replacement- cost coverage, your house and belongings will be replaced at today's cost.