The present article investigates possibilities and limits of local (shallow) analysis of discourse coherence with respect to the phenomena of global coherence and higher composition of texts. We study corpora annotated with local discourse relations in Czech and partly in English to try and find clues in the local annotation indicating a higher discourse structure. First, we classify patterns of subsequent or overlapping pairs of local relations, and hierarchies formed by nested local relations. Special attention is then given to relations crossing paragraph boundaries and their semantic types, and to paragraph-initial discourse connectives. In the third part, we examine situations in which annotators incline to marking a large argument (larger than one sentence) of a discourse relation even with a minimality principle annotation rule in place. Our analyses bring (i) new linguistic insights regarding coherence signals in local and higher contexts, e.g. detection and description of hierarchies of local discourse relations up to 5 levels in Czech and English, description of distribution differences in semantic types in cross-paragraph and other settings, identification of Czech connectives only typical for higher structures, or the detection of prevalence of large left-sided arguments in locally annotated data; (ii) as another type of contribution, some new reflections on methodologies of the approaches under scrutiny