Birmingham City Council has agreed to change the employee payments. If approved next month, about 26,000 staff could be affected as the council looks to save £212m in 2011/12.
Unions have warned of industrial action after the council said on Friday that 7,000 jobs must go by 2015.
Workers could now be asked to work evenings or weekends for no extra money, Roger Jenkins from the GMB said.
The lowest paid workers would be most affected, he added.
Some 30 union officials and workers lobbied councillors ahead of the cabinet meeting on Monday.