Interpreting performance is shaped by three major forces: a) the interpreter’s interpreting competence, b) cognitive conditions on-site and c) norms of interpreting. This research is a descriptive study of norms in the Chinese-English interpreting of Chinese Premier Press Conferences, which reveals the actual norms of consecutive interpreting especially with regard to source text and target text relations. It employs the research paradigm of descriptive translation studies and the analytic tool of shifts. Through inter-textual comparative analysis of the parallel corpus of the on-site interpretation of 11 Chinese Premier Press Conferences (1998-2008), three types of shifts are identified, including Type A shifts (Addition), Type R shifts (Reduction) and Type C’ shifts (Correction). With quantitative statistics of the regularity of the occurrences of shifts and qualitative analysis of every type of shifts in the corpus, four typical norms of ST-TT relations are identified: a) the norm of adequacy, b) the norm of explicitation in logic relations, c) the norm of specificity in information content, d) the norm of explicitness in meaning. This descriptive study of norms based on a relatively large corpus of on-site interpretation can serve as a tentative exploration of the methodology in descriptive interpreting studies. It may also shed new light on interpreting quality studies.