[en] The penetrability is computed exactly through two-peaked fission barriers consisting of three smoothly joined parabolic segments by evaluating accurately the Weber's cylinder functions appearing in the exact formulation of Cramer and Nix. When this is compared with the penetrability obtained in the WKB approximation for an identical potential barrier, it is found that the WKB transmission resonances within the intermediate well exhibit variable amounts of energy shifts from the exact resonances as large as 150 keV for narrow wells, for incident energies between the top and the bottom of the well. To illustrate the overall performance of the WKB method as an approximation to fission penetrability calculations, the ratio of penetrabilities by the WKB and the exact methods is graphically presented for all the allowed incident energies. The influence of curvature of the intermediate well, and of adjacent barriers on energy shifts is examined in detail. It is found that the use of accurate values of Weber's function yields spontaneous fission half-lives which are about 10% higher than the values reported by Cramer and Nix