  We propose a new strategy for the determination of the step scaling function
$\sigma(u)$ in finite size scaling studies using the Gradient Flow. In this
approach the determination of $\sigma(u)$ is broken in two pieces: a change of
the flow time at fixed physical size, and a change of the size of the system at
fixed flow time. Using both perturbative arguments and a set of simulations in
the pure gauge theory we show that this approach leads to a better control over
the continuum extrapolations. Following this new proposal we determine the
running coupling at high energies in the pure gauge theory and re-examine the
determination of the $\Lambda$-parameter, with special care on the perturbative
truncation uncertainties.
