  We analyze stationary slicings of the Schwarzschild spacetime defined by
members of the Bona-Masso family of slicing conditions. Our main focus is on
the influence of a non-vanishing offset to the extrinsic curvature, which
forbids the existence of standard Cauchy foliations but at the same time allows
gauge choices that are adapted to include null infinity (scri) in the
evolution. These hyperboloidal slicings are especially interesting for
observing outgoing gravitational waves. We show that the standard 1+log slicing
condition admits no overall regular hyperboloidal slicing, but by appropriately
combining with harmonic slicing, we construct a gauge condition that leads to a
strongly singularity-avoiding hyperboloidal foliation that connects the black
hole to scri.

General Relativity and Quantum Cosmology