NEW YORK » More than 20,000 AT&T workers in California, Nevada and Connecticut started two-day strikes Tuesday to protest what the union called harassment by the company.

The phone company is negotiating new contracts with the Communications Workers of America. The company is restricting standard bargaining-support activities such as wearing union stickers and buttons, said Libby Sayre, president of the CWA district covering California and Nevada.

Unlike a bargaining strike of indefinite duration, this one is limited but extendable, Sayre said.

AT&T spokesman Marty Richter said the company has been "negotiating in good faith."

The workers are on the landline side of the company. Richter said the company was well prepared to handle the disruption.

In June, an unknown number of workers in California and Nevada walked off the job to protest a memo that the union says impugned their work performance. That work stoppage lasted a day and wasn’t as broadly organized as Tuesday’s.

The contracts expired in April, and negotiations have been going on since February.

At issue in the negotiations are job protection clauses and health care premiums and co-payments. AT&T says it wants employees to shoulder more of their growing health care costs and wants more leeway to downsize its shrinking landline operations. Some of its workers have contracts that guarantee them job offers at different parts of the company if they’re laid off.

Union organizers point to the overall financial health of the company, which posted a profit of $4 billion for last year.

On Monday, AT&T reached a tentative agreement with CWA’s Southeast district, covering former BellSouth territory and 22,000 landline workers.

Dallas-based AT&T Inc. is the country’s largest employer of unionized workers. About 140,000 of its 256,000 employees are union members.