A new proposal from the Cyprus finance ministry says bank depositors with savings of 20,000 euros (£17,000) or less would be exempt from a levy.
Amounts between 20,000 and 100,000 euros would face a 6.75% tax. The levy on savings above 100,000 would remain at 9.9%. The levy has enraged Cypriots.
The earlier plan was to tax all savings under 100,000 euros at 6.75%.
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.
Late on Monday the eurozone finance ministers urged Cyprus to rethink the levy on bank deposits, which had been agreed on Saturday in Brussels.
Fearing a run on accounts, Cyprus has shut its banks until at least Thursday. The local stock exchange also remains closed.
President Nicos Anastasiades has urged all parties to back the bailout, saying Cyprus will be bankrupt if the deal does not go ahead.
