The plan was changed following outrage that ordinary savers would be forced to pay a levy of 6.75%.
The new plan would keep that levy on deposits over 20,000 euros, with those over 100,000 euros charged at 9.9%.
The controversial tax is a condition for Cyprus to get a 10bn-euro loan from the EU and IMF, to rescue its banks.
A crucial vote is looming in the Cypriot parliament on the bailout deal - expected to start at 18:00 (16:00 GMT). But there is still much uncertainty, and it is expected to be very close.
President Nicos Anastasiades has urged all parties to back the bailout, saying Cyprus will be bankrupt if the deal does not go ahead.
The Cyprus central bank chief, Panicos Demetriades, has warned that scrapping the tax on small savers would scupper the plan to raise 5.8bn euros in total from bank deposits. He also predicted account holders could suddenly withdraw 10% or more of the total in Cypriot banks if the levy was imposed.
At the same time, Mr Demetriades said he favoured imposing the levy only on accounts above 100,000.