Multi-frequency, multi-epoch ATCA observations of a sample of AGN resulted in the identification of nine new candidate Giga-hertz Peaked Spectrum sources. Here, we present Long Baseline Array observations at 4.8 GHz of the four candidates with no previously published VLBI image, and consider these together with previously published VLBI images of the other five sources. We find core-jet or compact double morphologies dominate, with further observations required to distinguish between these two possibilities for some sources. One of the nine candidates, PKS 1831–711, displays appreciable variability, suggesting its GPS spectrum is more ephemeral in nature. We focus in particular on the apparent relationship between a narrow spectral width and ‘compact double’ parsec-scale morphology, finding further examples, but also exceptions to this trend. An examination of the VLBI morphologies high-redshift (z > 3) sub-class of GPS sources suggests that core-jet morphologies predominate in this class.