  The peculiar features of quantum magnetism sometimes forbid the existence of
gapped `featureless' paramagnets which are fully symmetric and
unfractionalized. The Lieb-Schultz-Mattis theorem is an example of such a
constraint, but it is not known what the most general restriction might be. We
focus on the existence of featureless paramagnets on the spin-1 square lattice
and the spin-1 and spin-1/2 honeycomb lattice with spin rotation and space
group symmetries in 2+1D. Although featureless paramagnet phases are not ruled
out by any existing theorem, field theoretic arguments disfavor their
existence. Nevertheless, by generalizing the construction of Affleck, Kennedy,
Lieb and Tasaki to a class we call `slave-spin' states, we propose featureless
wave functions for these models. The featureless-ness of the spin-1 slave-spin
states on the square and honeycomb lattice are verified both analytically and
numerically, but the status of the spin-1/2 honeycomb state remains unclear.
