The present numerical study examines bifurcation sequences in Rayleigh-Benard convection for small aspect ratio enclosures. The three-dimensional rectangular enclosure has insulated sidewalls. The top wall is cooled and the bottom wall is heated, both isothermally. The Boussinesq approximation is invoked with the exception of temperature dependent viscosity of the fluid. The numerical simulations closely model specific experiments. Accordingly, the mean Prandtl number is set to 5 and the aspect ratios are set to 2.42 and 1.23. The computations exactly match the bifurcation sequence observed in the experiments while increasing the Rayleigh number, which is steady state --> periodic --> quasi-periodic --> steady state. It is established that the counter-intuitive transition from quasi-periodic to steady dynamical behavior with an increase in Rayleigh number is due to spatial changes in the mean velocity and temperature fields that accompany the bifurcation. The computations span a range of Rayleigh numbers from 2.5 x 10(3) to 1.3 x 10(5). Both unsteady and steady thermal convection are examined in detail.