We report spectroscopic characterization and unimolecular rectification (asymmetric electrical conduction) measurements of three donor-sigma-acceptor (D-sigma-A) compounds N-(10-nonadecyl)-N-(1-pyrenylmethyl)-perylene-3,4,9,10-bis(dicarboximide ) (1), N-(10-nonadecyl)-N-(4-[1-pyrenyl]butyl) perylene-3,4,9,10-bis(dicarboximide) (2), and N-(10-nonadecyl)-N-(2-ferrocenylethyl)perylene-3,4,9,10-bis(dicarboximid e) (3). These molecules were arranged as one-molecule thick Langmuir-Blodgett monolayers between Au electrodes. In such an "Au vertical bar D-sigma-A vertical bar Au" sandwich, molecule 1 is a unimolecular rectifier, with rather small rectification ratios (between 2 and 3 at +/- 1 V) that decrease upon cycling. Molecule 2 does not rectify. Molecule 3 rectifies, with a rectification ratio of between 14 and 28 at +/- 1 V; the through-film rectification and currents persist, even with scans of +/- 2 V, for up to 40 cycles of measurement. Qualitative arguments, based on a two-level rectification mechanism, are consistent with the current asymmetries observed in the monolayers of 1 and 3.