The failure history of pre-existing systems can inform a reliability assessment of a new system. Such assessments – consisting of arguments based on evidence from older systems – are attractive and have been used for quite some time for, typically, mechanical/hardware-only systems. But their application to software-based systems brings some challenges. In this paper, we present a conservative, Bayesian approach to software reliability assessment – one that combines reliability evidence from an old system with an assessor’s confidence in a newer system being an improved replacement for the old one. We demonstrate, via different scenarios, what a thought-to-be-better replacement formally means in practice, and what it allows one to believe about actual reliability improvement. The results can be used directly in a reliability assessment, or to caution system stakeholders and industry regulators against using other models that give optimistic assessments. For instance, even if one is certain that some new software must be more reliable than an old product, using the reliability distribution for the old software as a prior distribution when assessing the new system gives optimistic, not conservative, predictions for the posterior reliability of the new system after seeing operational testing evidence.