  We explore the sensitivity of limb darkening coefficients computed from
stellar atmosphere models to different least-squares fitting methods. We
demonstrate that conventional methods are strongly biased to fitting the
stellar limb. Our suggested method of fitting by minimizing the radially
integrated squared residual yields improved fits with better flux conservation.
The differences of the obtained coefficients from commonly used values are
observationally significant. We show that the new values are in better
agreement with solar limb darkening measurements as well as with coefficients
reported from analyses of eclipsing binary light curves.
