  Determining neutron star (NS) radii and masses can help to understand the
properties of matter at supra-nuclear densities. Thermal emission during
thermonuclear X-ray bursts from NSs in low-mass X-ray binaries provides a
unique opportunity to study NS parameters, because of the high fluxes, large
luminosity variations and the related changes in the spectral properties. The
standard cooling tail method uses hot NS atmosphere models to convert the
observed spectral evolution during cooling stages of X-ray bursts to the
Eddington flux F_Edd and the stellar angular size \Omega. These are then
translated to the constraints on the NS mass M and radius R. Here we present
the improved, direct cooling tail method that generalises the standard
approach. First, we adjust the cooling tail method to account for the
bolometric correction to the flux. Then, we fit the observed dependence of the
blackbody normalization on flux with a theoretical model directly on the M-R
plane by interpolating theoretical dependences to a given gravity, hence
ensuring only weakly informative priors for M and R instead of F_Edd and
\Omega.
  The direct cooling method is demonstrated using a photospheric radius
expansion burst from SAX J1810.8--2609, which has happened when the system was
in the hard state. Comparing to the standard cooling tail method, the
confidence regions are shifted by 1 sigma towards larger radii, giving
R=11.5-13.0 km at M=1.3-1.8 M_sun for this NS.
