An algorithm for the computation of initial relaxation directions (IRD) from; the tip of a conical intersection is discussed. The steepest descent paths that can be computed starting from these IRD provide a description of the ground state relaxation of the "cold" excited state species that occur in organic photochemistry where slow motion and/or thermal equilibration is possible (such as in cool jet, in matrices, and in solution). Under such conditions we show that the central conclusions drawn from a search for IRD and those obtained from semiclassical trajectory computations are the same. In this paper, IRD computations are used to investigate the mechanism of photoproduct formation and distribution in the photolysis of cyclohexadiene (CHD) and cZc-hexatriene (cZc-HT). A systematic search for the IRD in the region of the 2A(1)/1A(1) conical intersection (see Celani, P.; Ottani, S.; Olivucci, M.; Bernardi, F.; Robb, M. A. J. Am. Chem. Sec. 1994, 116, 10141-10151) located on the 2A(1) potential energy surface of these systems yields three relaxation paths. The first two paths, which start in the strict vicinity of the intersection, are nearly equivalent energetically and lead to production of CHD and cZc-HT, respectively. The third path, which begins at a much larger distance, lies higher in energy and ends at a methylenecyclopentene diradical (MCPD) minimum. Further, while the first two paths define directions that form a 60 degrees angle with the excited state entry channel(i.e. the direction along where the conical intersection region is entered), the third path is orthogonal. It is shown that these findings are consistent with the experimental observations which show nearly equivalent quantum yields for CHD and cZc-HT and no production of MCPD. The results of the IRD computations have been validated by investigating the decay dynamics of trajectories starting from a "circle" of points around the conical intersection, with the initial kinetic energy distributed in randomly sampled vibrational modes. These computations have been carried out using a trajectory-surface-hopping (TSH) method and a hybrid molecular mechanics valence bond (MM-VB) force field to model the ab initio potentials.