Compression has been advocated as one of the principles which pervades inductive inference and prediction - and, from there, it has also been recurrent in definitions and tests of intelligence. However, this connection is less explicit in new approaches to intelligence. In this paper, we advocate that the notion of compression can appear again in definitions and tests of intelligence through the concepts of `mind-reading¿ and `communication¿ in the context of multi-agent systems and social environments. Our main position is that two-part Minimum Message Length (MML) compression is not only more natural and effective for agents with limited resources, but it is also much more appropriate for agents in (co-operative) social environments than ...