  The textbook effective-range expansion of scattering theory is useful in the
analysis of low-energy scattering phenomenology when the scattering length
$|a|$ is much larger than the range $R$ of the scattering potential: $|a|\gg
R$. Nevertheless, the same has been used for systems where the scattering
length is much smaller than the range of the potential, which could be the case
in many scattering problems. We suggest and numerically study improved
two-parameter effective-range expansions for the cases $|a| > R$ and $|a| < R$.
The improved effective-range expansion for $|a| > R$ reduces to the textbook
expansion for $|a|/R \gg 1$.
