Electricity disaggregation identifies individual appliances from one or more aggregate data streams and has immense potential to reduce residential and commercial electrical waste. Since supervised learning methods rely on meticulously labeled training samples that are expensive to obtain, unsupervised methods show the most promise for widespread application. However, unsupervised learning methods previously applied to electricity disaggregation suffer from critical limitations. This paper introduces the concept of iterative appliance discovery, a novel unsupervised disaggregation method that progressively identifies the 'easiest to find' or 'most likely' appliances first. Once these simpler appliances have been identified, the computational complexity of the search space can be significantly reduced, enabling iterative discovery to identify more complex appliances. We test iterative appliance discovery against an existing competitive unsupervised method using two publicly available datasets. Results using different sampling rates show iterative discovery has faster runtimes and produces better accuracy. Furthermore, iterative discovery does not require prior knowledge of appliance characteristics and demonstrates unprecedented scalability to identify long, overlapped sequences that other unsupervised learning algorithms cannot.