The company said that it had addressed all of Mr. Meyer’s concerns, and that he was fired for what the company said was a failure to cooperate in an internal investigation. Health Management fired the Gatrells, it said, “for performance issues,” an accusation Dr. Gatrell strongly denied.

Doctors at other hospitals also say they have faced pressure to meet financial targets. Dr. Manuel Abreu said his contract with All Care Medical Consultants, a practice in Clearwater, Fla., allowed him to earn a bonus as high as $5,000 if he kept patients’ hospital stays to an average of no more than three days, according to a copy of the contract included with a lawsuit he filed in Florida state court this year. The parties reached a settlement and the case was voluntarily dismissed, court records show. Calls to Dr. Abreu’s lawyer and a lawyer for All Care were not returned.

Other physicians say they are pushed to ignore what is best for patients by referring them to doctors working for the same hospital. Dr. Victoria Rentel, a family practice doctor near Columbus, Ohio, recalled feeling pressured when she was employed by a local hospital to send her patients to doctors there for tests and procedures.

“I routinely got reports about the money I kept in the system,” Dr. Rentel said, detailing how much revenue she was generating for the hospital through in-house referrals. “I tended to refer to specialists I knew who would deliver better care.” The hospital eventually closed the clinic where she worked.

Some physicians also complain about quotas. Dr. Patricia F. White, an emergency room physician who worked at Baptist Health in Jacksonville, Fla., said that starting in 2010, her compensation was partly calculated based on the number of patients she saw an hour, according to a lawsuit she filed in August against the hospital and Emergency Resources Group, which provided emergency room staffing to Baptist.

The staffing group said it had no choice but to agree to the hospital’s demands. “If we don’t comply with their wishes as good partners, there is a termination notice in our contract,” wrote Paul Davidson, administrator for the group, in a series of e-mails that were included with Dr. White’s lawsuit.

In an e-mailed statement, Baptist Health said that patients expected timely access to quality care and that an emergency room physician’s “productivity and efficiency are vital components to delivering good patient care as well as ensuring patient safety and satisfaction.” A lawyer for Emergency Resources Group echoed those sentiments in an e-mailed statement, adding that efficiency was only one component of physician compensation.