We have undertaken a detailed analysis of HST/WFPC2 and STIS imaging observations, and of supplementary wide-field ground-based observations obtained with the NTT of two young ~10-25 Myr) compact star clusters in the LMC, NGC 1805 and NGC 1818. The ultimate goal of our work is to improve our understanding of the degree of primordial mass segregation in star clusters. This is crucial for the interpretation of observational luminosity functions (LFs) in terms of the initial mass function (IMF), and for constraining the universality of the IMF. We present evidence for strong luminosity segregation in both clusters. The LF slopes steepen with cluster radius; in both NGC 1805 and NGC 1818 the LF slopes reach a stable level well beyond the clusters core or half-light radii. In addition, the brightest cluster stars are strongly concentrated within the inner ~4 R_hl. The global cluster LF, although strongly nonlinear, is fairly well approximated by the core or half-light LF; the (annular) LFs at these radii are dominated by the segregated high-luminosity stars, however. We present tentative evidence for the presence of an excess number of bright stars surrounding NGC 1818, for which we argue that they are most likely massive stars that have been collisionally ejected from the cluster core. We therefore suggest that the cores of massive young stars clusters undergo significant dynamical evolution, even on time-scales as short as ~25 Myr.