We consider the equations of linearised gravity on the Schwarzschild spacetime in a double null gauge. Applying suitably commuted versions of the conservation
laws derived in earlier work of the second author we establish control on the gauge
invariant Teukolsky quantities α[±2] without any reference to the decoupled Teukolsky
wave equation satisfied by these quantities. More specifically, we uniformly bound the
energy flux of all first derivatives of α[±2] along any outgoing cone from an initial data
quantity at the level of first derivatives of the linearised curvature and second derivatives
of the linearised connection components. Analogous control on the energy fluxes along
any ingoing cone is established a posteriori directly from the Teukolsky equation using
the outgoing bounds.