Integrated information theory (IIT) is a theory of consciousness that aims to bridge the gap between physics and phenomenology by studying how information is distributed and processed between parts of the brain. The core idea is that the neural dynamics underlying conscious states are characterised by a balance of segregation, to the extent that regions operate independently; and segregation, to the extent that the brain behaves as a cohesive whole. In mathematical terms, IIT provides two main tools: a scalar measure, Phi, that quantifies _how much_ information is integrated in the brain; and a topological object, called an Information Structure (IS), that describes _how_ this information is integrated. For the last 10 years, researchers have proposed multiple measures of integrated information, incorporating recent developments in information theory. In this work we perform a comprehensive study of integrated information measures in neuroimaging (MEG) data of subjects in the psychedelic state. As a first result, we report widespread changes in integration in theta activity, while integration in alpha activity remains unchanged, despite the strong power suppression typically associated with psychedelic neurodynamics. Furthermore, we examine the properties and the dynamics of the informational structures arising different brain networks, and compare them with results from other studies.