The failure circumstances of complex aviation systems involving technologies such as software are dominated by systematic faults. However, systematic faults are often poorly resolved by the coupling of software assurance with traditional system safety methodologies. This paper examines an alternative approach to the assurance of software against systematic faults in aviation systems. Earlier work in this body of research (refer to [ReM10]) proposed an assurance framework based on an Architectural Safety Assurance Level (ASAL). Furthering the earlier research, this paper proposes a Claims Safety Assurance Level (CSAL) and Evidence Safety Assurance Level (ESAL) concept that is compatible with the ASAL concept. The core idea behind claims assurance is to ensure that any assurance levels used for articulating claims assurance in the context of the ASAL have a specific product safety focus (i.e. each and every assurance level has a product meaning, not just a top-down or bottom up process interpretation). For evidence assurance, the core idea introduces the concept of ‘tolerability of limitations’. The ‘tolerability of limitations’ is intended to be a product behavioural measure of the ‘tolerability’ in the provision of suitable evidence, while explicitly taking into account any limitations / shortfalls in the provision of evidence. The ‘tolerability of limitations’ also takes into account any known product shortfalls/limitations. The intent of evidence assurance is to provide a framework that is explicit with respect to the ‘tolerability of limitations’ of evidence with respect to safety.