  One of the biggest problems we can encounter while dealing with the
limb-darkening coefficients for stellar atmospheric models with spherical
symmetry is the difficulty of adjusting both the limb and the central parts
simultaneously. In particular, the regions near the drop-offs are not well
reproduced for most models, depending on Teff, log g, or wavelength. Even if
the law with four terms is used, these disagreements still persist. Here we
introduce a new method that considerably improves the description of both the
limb and the central parts and that will allow users to test models of stellar
atmospheres with spherical symmetry more accurately in environments such as
exoplanetary transits, eclipsing binaries, etc.
  The method introduced here is simple. Instead of considering all the $\mu $
points in the adjustment, as is traditional, we consider only the points until
the drop-off ($\mu_{cri}$) of each model. From this point, we impose a
condition ${I(\mu)}/{I (1)} = 0$. All calculations were performed by adopting
the least-squares method.
  The resulting coefficients using this new method reproduce the intensity
distribution of the PHOENIX spherical models (COND and DRIFT) quite well for
the photometric systems of the space missions {{\sc TESS}}, {{\sc KEPLER}},
{{\sc COROT}}, and {{\sc MOST}}. The calculations cover the following ranges of
local gravity and effective temperatures:
  2.5 $\leq$ log g $\leq$ 6.0 and 1500 K $\leq$ T$_{\rm eff}$
  $\leq$ 12000 K. The new spherical coefficients can easily be adapted to the
most commonly used light curve synthesis codes.
