We present improvements to our incremental proposition-based summariser, which is inspired by Kintsch and van Dijk's (1978) text comprehension model. Argument overlap is a central concept in this summariser. Our new model replaces the old overlap method based on distributional similarity with one based on lexical chains. We evaluate on a new corpus of 124 summaries of educational texts, and show that our new system outperforms the old method and several stateof-the-art non-proposition-based summarisers. The experiment also verifies that the incremental nature of memory cycles is beneficial in itself, by comparing it to a non-incremental algorithm using the same underlying information.