An exponential decrease of molecular conductance with length has been observed in most molecular systems reported to date, and has been taken as a signature of non-resonant tunneling as the conduction mechanism. Surprisingly, the conductance of iodide-terminated oligothiophene molecules presented herein does not follow the simple exponential length dependence. The lack of temperature dependence in the conductance indicates that tunneling still dominates the conduction mechanism in the molecules. Transition voltage spectroscopy shows that the tunneling barrier of the oligothiophene decreases with length, but the decrease is insufficient to explain the non-exponential length dependence. X-ray photoelectron spectroscopy, stretching length measurement, and theoretical calculations show that the non-exponential length dependence is due to a transition in the binding geometry of the molecule to the electrodes in the molecular junctions as the length increases.