Following a nine-month investigation by New York Attorney General Andrew Cuomo, Verizon Wireless has agreed to reimburse $1 million to some of its subscribers after marketing a wireless Internet plan that fell short of its promises. The company had advertised an Unlimited National Access and Broadband Access plan for $59.99 a month, but when about 13,000 users attempted to take advantage of unrestricted bandwidth, they received letters terminating their service.

“When consumers are promised an ‘unlimited’ service, they do not expect the promise to be broken by hidden limitations,” Mr. Cuomo said in a statement on Tuesday.

The usage restrictions, which were outlined in the service agreement, prohibited online gaming and downloading video. Verizon Wireless sent termination letters to users who had downloaded more than 10 gigabytes per month, writing that they must have engaged in the prohibited activities.

An information technology consultant, Robert Temple, who filed the initial complaint, said it is theoretically possible to reach the high levels of downloads from regular browsing, adding that many major web sites now include streaming video on their pages.

Verizon Wireless said in a statement that they are beginning to update the advertising campaign for the plan and it will be available in the spring. The company is also required to pay a $150,000 fine to New York State.