To mitigate the potentially harmful effects of nonresponse, many surveys repeatedly follow up with nonrespondents, often targeting a particular response rate or predetermined number of completes. Each additional recruitment attempt generally brings in a new wave of data, but returns gradually diminish over the course of a fixed data collection protocol. This is because each subsequent wave tends to contain fewer and fewer new responses, thereby resulting in smaller and smaller changes on (nonresponse-adjusted) point estimates. Consequently, these estimates begin to stabilize. This is the notion of phase capacity, suggesting some form of design change is in order, such as switching modes, increasing the incentive, or, as is considered exclusively in this research, discontinuing the nonrespondent follow-up campaign altogether. This dissertation consists of three methodological studies proposing and assessing various techniques survey practitioners can use to formally test for phase capacity. One of the earliest known phase capacity testing methods proposed in the literature calls for multiply imputing nonrespondents' missing data to assess, retrospectively, whether the most recent wave of data significantly altered a key estimate. The first study introduces an adaptation of this test amenable to surveys that instead reweight the observed data to compensate for nonresponse. A general limitation of methods discussed in the first study is that they are applicable to a single point estimate. The second study evaluates two extensions, each with the aim of producing a universal, yes-or-no phase capacity determination for a battery of point estimates. The third study builds upon ideas of a prospective phase capacity test recently proposed in the literature attempting to address the question of whether an imminent wave of data will significantly alter a key estimate. All three studies include a simulation study and application using data from the 2011 Federal Employee Viewpoint Survey.