Unmanned Aircraft Systems (UASs) rely upon a significant amount of software. An appropriate authorizing agent must approve the use of the UAS in a desired environment before use, and the authorization approach used must contend with the UAS' software. Unfortunately, the variety of UAS types, the range ofenvironments within which they must operate, and the need to address both safety and security concerns make authorization of UAS software problematic. We have developed a flexible approach to UAS software authorization that is able to deal with these challenges. Our approach is based on rigorous fitness arguments that explain how evidence from the software's development shows that the software has the properties that make the UAS fit for use in the intended operating contexts. In this paper, we present the details of our approach, compare it to existing approaches, and show how retroactive construction of softwarefitness arguments can identify the additional evidence necessary to support full authorization or the limited authorization that can be granted based on existing evidence. We give examples to illustrate how our approach can be used across a wide variety of UASs, missions, and operating environments, including controlled airspace.