Fatty acid Langmuir-Blodgett films, a quartz crystal microbalance, and Fourier-transform infrared dichroism have been used to study the evolution of the melting transition upon the variation of the sample thickness, from bulk to a few monolayers. Whereas ordinary bulk behavior was observed for samples all the way down to n = 12 layers, a crossover range of 12 less than or equal to n less than or equal to 8 was identified to a continuous transition, characterized also by the existence of an intermediate orientationally ordered phase. Measurements on annealed samples indicated the strong sensitivity of such a phase and the order of the transition to defects and sample metastability.