  We consider a subclass of degenerate higher-order scalar-tensor (DHOST)
theories in which gravitational waves propagate at the speed of light and do
not decay into scalar fluctuations. The screening mechanism in DHOST theories
evading these two gravitational wave constraints operates very differently from
that in generic DHOST theories. We derive a spherically symmetric solution in
the presence of nonrelativistic matter. General relativity is recovered in the
vacuum exterior region provided that functions in the Lagrangian satisfy a
certain condition, implying that fine-tuning is required. Gravity in the matter
interior exhibits novel features: although the gravitational potentials still
obey the standard inverse power law, the effective gravitational constant is
different from its exterior value, and the two metric potentials do not
coincide. We discuss possible observational constraints on this subclass of
DHOST theories, and argue that the tightest bound comes from the Hulse-Taylor
pulsar.
