  Quantified modal logic provides a natural logical language for reasoning
about modal attitudes even while retaining the richness of quantification for
referring to predicates over domains. But then most fragments of the logic are
undecidable, over many model classes. Over the years, only a few fragments
(such as the monodic) have been shown to be decidable. In this paper, we study
fragments that bundle quantifiers and modalities together, inspired by earlier
work on epistemic logics of know-how/why/what. As always with quantified modal
logics, it makes a significant difference whether the domain stays the same
across worlds, or not. In particular, we show that the bundle $\forall \Box$ is
undecidable over constant domain interpretations, even with only monadic
predicates, whereas $\exists \Box$ bundle is decidable. On the other hand, over
increasing domain interpretations, we get decidability with both $\forall \Box$
and $\exists \Box$ bundles with unrestricted predicates. In these cases, we
also obtain tableau based procedures that run in \PSPACE. We further show that
the $\exists \Box$ bundle cannot distinguish between constant domain and
increasing domain interpretations.
