AT&T, the No. 2 U.S wireless provider, said on Wednesday that it would roll out a new data plan that does away with overage fees and reduces data speeds for wireless customers who surpass their data allowance. Beginning Sunday, customers can choose the new Mobile Share Advantage plan and pay for extra data, if needed, or work with slower data speeds instead of paying for overages, the company said in a statement. Its current plan includes a $5 data overage charge per 300 megabytes on its 300-megabyte plan and $15 per 1 gigabyte on other plans.

The move came after AT&T's bigger rival, Verizon Communications, announced a feature last month called "safety mode" that protects users against data overages and slows down speeds.

Both Verizon and AT&T have been reworking their plans as smaller competitors T-Mobile, which eliminated data overage charges in 2014, and Sprint, which offers half-off dicsounts, are luring customers away to their services, Entner added.

AT&T has also revised prices and data bucket sizes. For instance, its larger 25-gigabyte plan now costs $190 per month for four smartphone lines. It previously cost $235.

All the new plans include an access charge of $10 to $40 per month for each device, AT&T said.

The new plans will continue to have features such as unlimited text and talk and rollover data. Plans above 10 gigabytes also include unlimited talk and text to Mexico and Canada and no roaming charges in Mexico.