Questions were raised by AMs with regards to additional funding for the Hywel Dda Health Board in Ceredigion, Carmarthenshire and Pembrokeshire.
Finance Minister Jane Hutt was leading a debate on the supplementary budget for 2012/13, on 17 July 2012.
Conservative AM for Preseli Pembrokeshire welcomed the extra £80m for the Hywel Dda Health Board over four years, however raised deep concerns with regards to the state of the health board's finances in Wales.
Plaid Cymru AM Ieuan Wyn Jones also questioned the minister's incentive to provide this extra funding and asked her why other health boards had not been given the same amount.
Mr Jones said that health boards had been "bailed out" over the years and that he was "not convinced that it (the Welsh government) has the NHS finances under control".
On the same subject, Liberal Democrat AM Peter Black Peter said that he was "not opposed" to the extra funding for the Hywel Dda Health Board, but wanted to know what conditions were attached to this.
In her response to opposition concerns, Jane Hutt insisted Hywel Dda was facing "unique challenges" and stressed the need for financial stability to ensure "sustainability" for future years.