This paper presents a concrete experience of Knowledge Engineering, which, starting from a specific problem which occurred during the development of ASTRA, a knowledge-based system for preventive diagnosis of power transformers, turned out to provide significant insights concerning modeling of uncertain knowledge. In particular, it was observed that there are (at least) two conceptually distinct types of uncertainty affecting knowledge, namely uncertainty about applicability (A-uncertainty, for short) and uncertainty about validity (V-uncertainty, for short), which are different in nature and play different roles in uncertain reasoning. The concepts of A- and V-uncertainty are applicable in any context where uncertainty affecting domain knowledge can be ascribed to two kinds of sources: on the one hand, the existence of exceptions, on the other hand, deep-rooted doubts about the foundations themselves of the relevant domain knowledge. The introduction of these concepts allows one to define articulated uncertainty models, supporting the representation of the reasoning mechanisms used by experts in domains where both such uncertainty sources are present. This general claim was confirmed by the experience developed with ASTRA, where the explicit representation and management of A- and V-uncertainty enabled the correct treatment of some critical diagnostic cases.