  We have conducted fully relativistic simulations in a class of scalar-tensor
theories with derivative self-interactions and screening of local scales. By
using high-resolution shock-capturing methods and a non-vanishing shift vector,
we have managed to avoid issues plaguing similar attempts in the past. We have
first confirmed recent results by ourselves in spherical symmetry, obtained
with an approximate approach and pointing at a partial breakdown of the
screening in black-hole collapse. Then, we considered the late inspiral and
merger of binary neutron stars. We found that screening tends to suppress the
(subdominant) dipole scalar emission, but not the (dominant) quadrupole scalar
mode. Our results point at quadrupole scalar signals as large as (or even
larger than) in Fierz-Jordan-Brans-Dicke theories with the same conformal
coupling, for strong-coupling scales in the MeV range that we can simulate.
