Research software projects often are initially funded by a grant that supports development of the software. But when the grant ends, the projects have to shift to another model to support the required software maintenance, if the software is going to continue being used. This talk will look at the Parsl project and its effort to become sustainable, across a set of project phases. It will also look at the different kinds of RSE work that have taken place during the project. These activities, phases, and developer types appear to be useful concepts for planning or studying other research software projects, or research software as a whole.