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The financial services industry has been among the slowest to embrace the mobile and other technologies that many consumers crave. Within the industry, insurers probably have been slowest—and their old-fashioned ways are stirring a high level of churn.

Insurance customers are generally pleased with their provider. Only 14% of those who submitted a claim in the past two years are unhappy with how it was handled, according to a report from Accenture. As you might expect, a high rate of those—83%—plan to switch providers. But even among the vast majority who filed a claim and were satisfied, 41% say they are likely to switch insurers in the next 12 months, the report found.

Why would satisfied customers switch? In general, their claims experience, while satisfactory, left them feeling it should have been better. “The bar has been raised and insurers now need to handle claims in a way that not only satisfies policyholders but also differentiates them from other insurers,” says Michael Costonis, global head of claims services at Accenture, a research and consulting firm.

Technology exists that would greatly streamline the claims process, he says. Consumers understand that, and when they file a claim and confront the old way of doing things they resolve to look for something better. For example, Costonis says, in the case of an auto accident, sensors could summon assistance automatically, notify a garage, and get a tow truck on the scene—all without a phone call. Your car could be fixed and delivered to your door, and if any money was due to you it might be put in your account without the tedious paperwork.

Customers expect quick claims and fair pricing. But they also want transparency and this is where technology can make a big difference. “More and more, especially with younger customers, this takes the form of providing anywhere, anytime access online or through mobile apps,” Costonis says. In the study, 44% said they would switch providers to be able to use digital channels to monitor the claims process.

Broader use of technology could help in other ways too. Three in four customers are willing to share more personal information in order to get better rates, the study found. Insurers could easily gather information about the condition of cars and customer driving habits. They could also gather information collected by smoke, carbon monoxide, humidity, and motion detectors. Such data could help them help their customers manage risks and wind up filing fewer claims—and that is the Holy Grail because customers hate the process and insurers lose a high percentage of those who file a claim no matter what.

Related: How to make sure you have enough insurance coverage