Detailed understanding of growth mechanisms in organic thin-film deposition is crucial for tailoring growth morphologies, which in turn determine the physical properties of the resulting films. For growth of the rodlike molecule para-sexiphenyl, the evolution of terraced mounds is observed by atomic force microscopy. Using methods established in inorganic epitaxy, we demonstrate the existence of an additional barrier (0.67 electron volt) for step-edge crossing-the Ehrlich-Schwoebel barrier. This result was confirmed by transition state theory, which revealed a bending of the molecule at the step edge. A gradual reduction of this barrier in the first layers led to an almost layer-by-layer growth during early deposition stage. The reported phenomena are a direct consequence of the complexity of the molecular building blocks versus atomic systems.