Recent work on two-phase free boundary problems has led to the investigation of a new type of quadrature domain for harmonic functions. This talk will discuss such two-phase quadrature domains and, in particular, how they may be constructed. The construction is based on the technique of partial balayage, which has proven to be a useful tool in the study of one-phase quadrature domains and Hele-Shaw flows. (Joint work with Tomas Sjodin.)