This paper presents a new type of nonlinear discourse structure found to be very common in free English texts. This structure reflects nonlinear presentation of the information and knowledge conveyed by the texts. It is argued that such nonlinearity is representationally and informationally advantageous because it allows one to create smaller, more compact texts. The paper presents a heuristics-based, relatively domain-independent algorithm for computing this new text structure. The paper discusses good quantitative and qualitative performance of the algorithm, and presents the results of the extensive tests on a large volume of free English texts.