In recent years, computer simulations have found increasingly widespread use as powerful tools for studying phase transitions in wide variety of systems. In the particular and very important case of aqueous systems, the commonly used force-fields tend to offer quite different predictions with respect to a wide range of thermodynamic and kinetic properties, including the ease of ice nucleation, the propensity to freeze at a vapor–liquid interface, and the existence of a liquid–liquid phase transition. It is thus of fundamental and practical interest to understand how different features of a given water model affect its thermodynamic and kinetic properties. In this work, we use the forward-flux sampling technique to study the crystallization kinetics of a family of modified Stillinger–Weber (SW) potentials with energy (ε) and length (σ) scales taken from the monoatomic water (mW) model, but with different tetrahedrality parameters (λ). By increasing λ from 21 to 24, we observe the nucleation rate increases by 48 orders of magnitude at a supercooling of ζ = T/T_m = 0.845. Using classical nucleation theory, we are able to demonstrate that this change can largely be accounted for by the increase in |Δμ|, the thermodynamic driving force. We also perform rate calculations in freestanding thin films of the supercooled liquid, and observe a crossover from surface-enhanced crystallization at λ = 21 to bulk-dominated crystallization for λ ≥ 22.