Universal Conceptual Cognitive Annotation (UCCA) is a semantic annotation scheme that organizes texts into coarse predicate-argument structure, offering broad coverage of semantic phenomena. At the same time, there is still need for a finer-grained treatment of many of the categories. The Adverbial category is of special interest, as it covers a wide range of fundamentally different meanings such as negation, causation, aspect, and event quantification. In this paper we introduce a refinement annotation scheme for UCCA's Adverbial category, showing that UCCA Adverbials can indeed be subcategorized into at least 7 semantic types, and doing so can help clarify and disambiguate the otherwise coarse-grained labels. We provide a preliminary set of annotation guidelines, as well as pilot annotation experiments with high inter-annotator agreement, confirming the validity of the scheme.