Core formation initiated in asteroid-sized bodies (planetesimals) within 1 Myr of the formation of the first solids in our solar system. Although this process left a lasting geochemical fingerprint on the composition of larger rocky planets such as Earth, we know surprisingly little about the segregation processes involved. One additional complication is that under the relatively low pressures of planetesimal interiors (a few GPa), mixing of light elements such a S, C, O, and P in core-forming, iron-rich liquids is highly non-ideal. In light element-rich liquids, this non-ideality can result in immiscibility, or unmixing of liquids. Here, we present results from experiments which constrain the extent of liquid immiscibility in realistic planetesimal core compositions, under moderate pressure/high temperature conditions of planetesimal interiors. Immiscibility results in separation of what we term Fe-rich (P-rich, C-rich, S-poor, O-poor) and FeS-rich (O-rich, P-poor, C-poor) liquids. Using meteoritic data to constrain the range of core-forming liquid compositions within planetesimals, we argue that the extent of immiscibility was controlled bulk planetesimal chemistry and thermal history, i.e. degree of volatile/light element loss (C, P, S, N etc) during heating and melting. Independently constraining the extent of immiscibility provides will provide insight into degassing processes during planetary formation, including rapid (Myr) melting and differentiation of rocky planetesimals in the early solar system, and the much slower (Gyr) differentiation of icy-rocky satellites in the outer solar system.