Spin-2 fields on Minkowski space near spacelike and null infinity

We show that the spin-2 equations on Minkowski space in the gauge of the ʹregular finite initial value problem at spacelike infinityʹ imply estimates which, together with the transport equations on the cylinder at spacelike infinity, allow us to obtain for a large class of initial data information on the smoothness of the solution near spacelike and null infinity of any desired precision.