Consultations have begun over plans to cut nearly 40 jobs at the Royal Cornwall Hospitals Trust.
The trust said it was talking to staff and their representatives over the possible loss of 38 posts in management and administration.
It added that redeployment options would also be looked at.
The trust plans to cut the equivalent of more than 400 jobs to help fill black holes in finances. It needs to make savings of £19m in 2011.
Human resources director Jon Sparkes said: "We will continue to make every effort to redeploy people, utilise natural turnover as well as voluntary redundancy to avoid compulsory redundancy whenever possible."
However, the trust added it could not rule out further job losses later in the year.
The posts did not include ward-based staff, it said.
Christine Dayus from the union Unison said staff were keen to know how the posts were being selected.
She said: "The job losses are going to be across a number of different departments.
"There will be consultation so we can test why particularly those posts have been identified.
"We also want to ensure the trust will deliver what they claim they will deliver, and assess the impact of how the duties are going to be performed."
The trust - which operates Truro's Royal Cornwall Hospital, West Cornwall Hospital in Penzance and St Michael's Hospital in Hayle - has about 5,000 staff and an annual budget of £290m.