  The concept of Floquet engineering is to subject a quantum system to
time-periodic driving in such a way that it acquires interesting novel
properties. It has been employed, for instance, for the realization of
artificial magnetic fluxes in optical lattices and, typically, it is based on
two approximations. First, the driving frequency is assumed to be low enough to
suppress resonant excitations to high-lying states above some energy gap
separating a low energy subspace from excited states. Second, the driving
frequency is still assumed to be large compared to the energy scales of the
low-energy subspace, so that also resonant excitations within this space are
negligible. Eventually, however, deviations from both approximations will lead
to unwanted heating on a time scale $\tau$. Using the example of a
one-dimensional system of repulsively interacting bosons in a shaken optical
lattice, we investigate the optimal frequency (window) that maximizes $\tau$.
As a main result, we find that, when increasing the lattice depth, $\tau$
increases faster than the experimentally relevant time scale given by the
tunneling time $\hbar/J$, so that Floquet heating becomes suppressed.
