The electrical conductance of a series of thiol-terminated alkanes, (1,6-hexanedithiol (HDT), 1,8-octanedithiol (ODT), and 1,10-decanedithol (DDT)) was measured using a modified scanning tunneling microscope break junction technique. The interpretation of data obtained in this technique is complicated due to multiple effects such as microscopic details of the metal-molecule junctions, superposition of tunneling currents, and conformational changes in the molecules. A new method called the last-step analysis (LSA) is introduced here to clarify the contribution of these effects. In direct contrast to previous work, LSA does not require any data preselection, making the results less subjective and more reproducible. Finally, LSA was used to obtain the conductance of single molecules (HDT, (3.6 x 10(-4))G(o); ODT, (4.4 x 10(-5))G(o); DDT, (5.7 x 10(-6))G(o)). The tunneling decay parameter (beta) was calculated, and it was found to be approximately 1.0 per carbon atom.