  By using 14 different versions and parametrizations of a proximity potential
and two new versions of the potential proposed in this paper, we perform a
comparative study of fusion barriers by studying 26 symmetric reactions. The
mass asymmetry $\eta_{A}$ = $(\frac{A_{2}-A_{1}}{A_{2}+A_{1}}),$ however, is
very large. Our detailed investigation reveals that most of the proximity
potentials reproduce experimental data within $\pm$8% on the average. A
comparison of fusion cross sections indicates that Bass 80, AW 95, and Denisov
DP potentials have a better edge than other potentials. We also propose new
versions of the proximity potential as well as Denisov parametrized potential.
These new versions improve the agreement with the data.
