NEW YORK >> AT&T is reducing cellphone rates for family plans with large amounts of data.

The new rates are available starting Sunday and apply to plans with at least 10 gigabytes of data shared by two or more phones on a single account. Savings start at $10 per phone per month. A family of four sharing 10 gigabytes will pay $160 a month combined instead of $200 under the most recent rates.

The changes represent AT&T’s latest effort to get customers to pay more overall by upgrading from lower-use plans. In some cases, families will actually pay less if they upgrade. That family of four, for instance, already pays $170 monthly for a 4 gigabyte plan and $180 for 6 gigabytes. If they upgrade, they will pay just $160. But for the most part, more data means more revenue for AT&T Inc.

David Christopher, chief marketing officer for AT&T’s wireless business, said the offer is designed to give families a worry-free experience as they consume more data for video and social networking.

It also could encourage people to add tablets to their accounts, as those consume even more data and would quickly use up allotments in the lower-use plans.

The new rates will also help AT&T wean people off subsidies on new phones. Instead of having people buy phones for $100 or $200 and having the true cost baked in to monthly service fees, AT&T and other carriers have been encouraging customers to pay the full price for phones outright or in installments.

Many people are already doing that, through programs such as AT&T’s Next, even though in many cases, it’s actually cheaper for people to use the subsidies for high-end phones as long as they keep their phones for two years or longer. Christopher said many customers prefer the flexibility of being able to upgrade as soon as Apple or Samsung releases a new model. Subsidized plans typically require customers to wait two years.

AT&T will let existing subsidized customers take advantage of the new rates, but when they are eligible for an upgrade, they must pay full price for the phone to keep the lower rates. New customers won’t be eligible for subsidies to get these rates.

AT&T is the second-largest cellphone company in the U.S. after Verizon Wireless.