Although most Catholic priests in the US say that they are “flourishing,” only 24% have confidence in their bishops, according to a new study from Catholic university.

The survey by the university’s sociology department, reflecting responses from 3,500 priests, found that American priests are particularly concerned about being falsely charged with sexual abuse. Only a bare majority (51%) believed that their bishops would support them in the face of false charges, and just 36% were confident that they would receive sufficient help to fight charges in court.

Many priests (45%) said that they were working under stress, with young priests more likely to report such problems. Less than two-thirds (63%) of those surveyed were satisfied with the support they received from their bishops.