Slab width plays a major role in controlling subduction dynamics and trench motion. However, observations on natural narrow subduction zones do not show any correlation between slab width and trench velocities, indicating that other factors may have a greater impact. Here, we use 3D numerical subduction models to evaluate the effect of slab width, strength of slab coupling to the lateral plate and overriding plate thickness on trench kinematics. Model results show that slab width has little influence on trench migration rates for narrow subduction zones, but that the thickness of the overriding plate plays a major role, with trench velocities decreasing as the thickness increases. These results explain trench velocities observed in natural narrow subduction zones showing no relation with slab width but an inverse dependence on overriding plate thickness. Finally, we find that the overriding plate thickness also significantly affects the trench shape.