A new Monte Carlo algorithm is presented for the simulation of atomistically detailed alkanethiol self-assembled monolayers (R-SH) on a Au(111) surface. Built on a set of simpler but also more complex (sometimes nonphysical) moves, the new algorithm is capable of efficiently driving all alkanethiol molecules to the Au(111) surface, thereby leading to full surface coverage, irrespective of the initial setup of the system. This circumvents a significant limitation of previous methods in which the simulations typically started from optimally packed structures on the substrate close to thermal equilibrium. Further, by considering an extended ensemble of configurations each one of which corresponds to a different value of the sulfur-sulfur repulsive core potential, sigma(ss), and by allowing for configurations to swap between systems characterized by different sigma(ss) values, the new algorithm can adequately simulate model R-SH/Au(111) systems for values of as, ranging from 4.25 angstrom corresponding to the Hautman-Klein molecular model (J. Chem. Phys. 1989, 91, 4994; 1990, 93, 7483) to 4.97 angstrom corresponding to the Siepmann-McDonald model (Langmuir 1993, 9, 2351), and practically any chain length. Detailed results are presented quantifying the efficiency and robustness of the new method. Representative simulation data for the dependence of the structural and conformational properties of the formed monolayer on the details of the employed molecular model are reported and discussed; an investigation of the variation of molecular organization and ordering on the Au(1 11) substrate for three CH3-(CH2)(n)-SH/Au(111) systems with n = 9, 15, and 21 is also included.