Alkanes on water show a two-stage wetting transition. Upon raising the temperature, a first-order transition from a molecularly thin to a mesoscopically thick liquid film is followed by a continuous divergence of the film thickness. This second transition is brought about by long-range interactions between adsorbate and substrate and is, therefore, referred to as long-range critical wetting. The divergence of the film thickness is theoretically expected to occur according to the asymptotic power law l∼(Tw,c−T)βs, with βs=−1. This value has indeed been found for pentane on pure water; however, for hexane on salt solutions of different concentrations, βs=−0.73 was found for a 1.5M solution of NaCl and βs=−0.57 for a 2.5M salt solution. In addition, for hexane on a 2.5M solution of NaCl, an exponent of αs=0.1 was found from contact-angle measurements, differing greatly from the theoretically expected value of αs=−1. Using Dzyaloshinskii-Lifshitz-Pitaevskii theory, we calculate effective local exponents in order to explain the experimental findings. Taking into account the uncertainty of the exponents derived from experiments as well as the temperature range in which the measurements were carried out, a reasonable agreement between theory and experiment is found, thereby providing a consistent approach to resolving the apparently anomalous behavior of hexane on brine. The experimentally observed exponents βs=−0.57 and αs=0.1 are also compatible with a long-range tricritical wetting transition, which is characterized by βs=−1/2 and αs=0; this alternative explanation of the experimental findings is neither supported nor completely ruled out by our calculations.