  In this paper, we present an improved parameterization of the elastic
scattering of spin-0 particles, which is based on a dispersive representation
for the inverse scattering amplitude. Besides being based on well known general
principles, the requirement that the inverse amplitude should satisfy the
dispersion relation significantly constrains its possible forms and have not
been incorporated in the existing parameterizations so far. While the
right-hand cut of the inverse scattering amplitude is controlled by unitarity,
the contribution from the left-hand cut, which comes from the crossing
symmetry, is commonly ignored or incorporated improperly. The latter is
parameterized using the expansion in a suitably constructed conformal variable,
which accounts for its analytic structure. The correct implementations of the
Adler zero and threshold factors for angular momentum $J>0$ are discussed in
detail as well. The amplitudes are written in a compact analytic form and
provide a useful tool to analyze current and future lattice data in the elastic
region improving upon the commonly used Breit-Wigner or K-matrix approaches.
