[1] Several models have been proposed to relate slab geometry to parameters such as plate velocity or plate age. However, studies on the observed relationships between slab geometry and a wide range of subduction parameters show that there is not a simple global relationship between slab geometry and any one of these other subduction parameters for all subduction zones. Numerical and laboratory models of subduction provide a method to explore the relative importance of different physical processes in determining subduction dynamics. Employing 2-D numerical models with a viscosity structure constrained by laboratory experiments for the deformation of olivine, we show that the observed range in slab dip and the observed trends between slab dip and convergence velocity, subducting plate age, and subduction duration can be reproduced without trench motion (i.e., slab roll-back) for locations away from slab edges. Successful models include a stiff slab that is 100-1000 times more viscous than previous estimates from models of plate bending, the geoid, and global plate motions. We find that slab dip in the upper mantle depends primarily on slab strength and plate boundary coupling, with a small dependence on subducting plate age. Once the slab sinks into the lower mantle the primary processes controlling slab evolution are (1) the ability of the stiff slab to transmit stresses up dip, (2) resistance to slab descent into the higherviscosity lower mantle, and (3) subduction-induced flow in the mantle-wedge corner.