  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 $\alpha^{[\pm 2]}$ 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 $\alpha^{[\pm 2]}$ 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.
