Parking restrictions are being introduced in residential areas close to the Worcestershire Royal Hospital.
A lack of spaces has led many people to park in nearby Warndon, which Worcester City Council says is dangerous.
Local residents, however, fear that new yellow lines will not solve the problem - and only shift it to another district.
Worcester City Council's senior engineer in transportation and traffic management Tom Comerford said he believed yellow lines were the best way to deal with dangerous parking.
But Councillor Mike Layland urged hospital management to meet with the city council to sort out the traffic problems that exist.
Parking space at the hospital is at such a premium that medical staff, as well as visitors, are using adjoining streets.