The amendments set a legal framework for the sharing of burdens, making it possible to continue the restructuring of the banking system, Finance Ministry State Secretary Mateja Vraničar told MPs.
Under the changes, the bail-in would affect shareholders and holders all junior debt instruments.
A bail-in would be an extraordinary measure in the event of heightened risk that a bank did not meet minimum capital requirements or could run afoul of such requirements within six months, and if it met insolvency criteria.
The conditions and the extent of the bail-in would be determined by the central bank.
The proposal is in line with the EU-wide banking rules that stepped into force on 1 August with a view to reduce the public cost of bank restructuring, though member states have until 2016 to make them part of their national law.
The amendments are being adopted primarily to reduce the cost of the winding down of two small banks, Probanka and Factor banka, which are already in the process of liquidation.
However, given the majority view that several more banks could need help, the holders of junior debt of other banks may be affected as well.
The legislation will be challenged by the Small Shareholders of Slovenia (MDS), which plans to seek a National Council veto and then turn to the Constitutional Court in the event the veto is overturned.
The association has argued that the holders of junior debt instruments were willing to accept a haircut but opposed being wiped out altogether.
The debate today showed apprehension in the ranks of the opposition, which raised some of the same concerns as the small shareholders.
New Slovenia (NSi) MP Matej Tonin thus wondered why the bail-in rules should apply to all banks if EU guidelines require their implementation only for systemic banks.
People's Party (SLS) president Franc Bogovič meanwhile argued that there was no rush to implement the rules, saying Slovenia could wait for the results of the ongoing bank stress tests to see exactly how much additional capital the banks will need.
The Democrats (SDS) meanwhile sought to insert an amendment that would abolish bank secrecy requirements if the data were to be requested by a parliamentary working body in order to pinpoint those culpable for the banking mess.
The coalition rejected this motion.