A contract with Interserve, which started last August, was terminated because detailed target costs were significantly higher than planned.
Refurbishing the 15th Century Guildhall, which sits alongside the River Ouse, was first billed to cost around £9m.
Now the city council has reviewed options, revising the scale and scope but the revised project is still expected to cost £4m-£5m more than originally budgeted.
Plans to build a roof terrace and insist on construction deliveries by river have been scrapped.
It now expects to retender the Grade 1 building revamp with shortlisted firms invited to tender in January for an 18-month project.