We investigate the sequence-dependent properties of proteins that determine the dual requirements of stability of the native stare and its kinetic accessibility using simple cubic lattice models. Three interaction schemes are used to describe the potentials between nearest neighbor nonbonded beads. We show that, under the simulation conditions when the native basin of attraction (NBA) is the most stable, there is an excellent correlation between folding times tau(F) and the dimensionless parameter sigma(T) = (T-theta-T-F)/T-theta, where T-theta is the collapse temperature and T-F is the folding transition temperature. There is also a significant correlation between tau(F) and another dimensionless quantity Z = (E-N-E-ms)/delta, where E-N is the energy of the native state, E-ms is the average energy of the ensemble of misfolded structures, and delta is the dispersion in the contact energies. In contrast, there is no significant correlation between tau(F) and the Z-score gap Delta(Z) = E-N - E-ms. An approximate relationship between sigma(T) and the Z-score is derived, which explains the superior correlation seen between tau(F) and sigma(T). For two state folders tau(F) is linked to the free energy difference (not simply energy gap, however it is defined) between the unfolded states and the NEA.