The orientation of alkanedithiol molecules in self-assembled monolayers (SAMs) is of vital importance for their transport properties in molecular junctions. It is demonstrated that a too-low concentration of long alkanedithiols in ethanol leads to the formation of looped molecules, resulting in a 50-fold increase of the current through the SAM. X-ray photoelectron spectroscopy measurements show that high-concentration dithiol solutions result in a preferential standing-up phase. To obtain an almost full standing-up phase of 1,14-tetradecanedithiol (C14) a 30 mM concentration in ethanol is required, whereas a 0.3 mM concentration leads to a highly looped monolayer. The conduction through the full standing-up phase of C14 and C16 is in accordance with the exponential dependence on molecule length as obtained from shorter alkanedithiols.