The surface tension $sigma$ of the confined-deconfined interface is calculated in pure $SU(3)$ lattice gauge theory at finite temperatures employing the operator and integral methods on a lattice of a size $8^2times N_ztimes 2$ with $N_z=16$ and 40. Analyses of non-perturbative corrections in asymmetry response functions strongly indicate that the use of one-loop values for the response functions lead to an overestimate of $sigma$ in the operator method. The operator method also suffers more from finite-size effects due to a finite thickness of the interface, leading us to conclude that the integral method yields more reliable values for $sigma$. Our result with the integral method $sigma/T_c^3=0.134(16)$ is consistent with earlier results and also with that obtained with a transfer matrix method. Result is also reported on $sigma$ obtained on a lattice $18^2times 48times 4$ with the integral method.
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