We study the pinch off dynamics of droplets of yield stress and shear thinning fluids. To separate the two non Newtonian effects, we use a yield stress material for which the yield stress can be tuned without changing the shear thinning behavior, and a shear thinning system (without a yield stress) for which the shear thinning can be controlled over a large range, without introducing too much elasticity into the system. We find that the pinch off remains very similar to that of constant viscosity Newtonian liquids, and consequently thinning in shear flow does not imply a thinning in elongational flow.