Cardelli and Gordon's calculus of Mobile Ambients has attracted widespread interest
as a model of mobile computation. The standard calculus is quite rich, with a variety
of operators, together with capabilities for entering, leaving and dissolving ambi-
ents. The question arises of what is a minimal Turing-complete set of constructs.
Previous work has established that Turing completeness can be achieved without
using communication or restriction. We show that it can be achieved merely using
movement capabilities (and not dissolution). We also show that certain smaller sets
of constructs are either terminating or have decidable termination.