Grafting a hyperbolic surface S along a weighted simple closed geodesic wC is the procedure of cutting the surface along the geodesic C and inserting a Euclidean cylinder of height w. For w > 0, this defines a grafting ray in Teichmueller space. For large values of w, the inserted annulus has large modulus, and it follows that the length of C goes to zero in the limit. On the other hand, the Teichmueller geodesic ray starting at S whose vertical foliation is e^t C also has the property that the length of C goes to zero as t goes to infinity. Motivated by this observation, we compare the grafting ray and Teichmueller ray and show that the distance between them with respect to the Teichmueller metric remains uniformly bounded. (Joint work with David Dumas and Kasra Rafi)