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We present Very Long Baseline Interferometry observations of a faint andlow-luminosity ($L_{\rm 1.4 GHz} < 10^{27}~\mbox{W Hz}^{-1}$) Gigahertz-PeakedSpectrum (GPS) and Compact Steep Spectrum (CSS) sample. We select eight sourcesfrom deep radio observations that have radio spectra characteristic of a GPS orCSS source and an angular size of $\theta \lesssim 2$ arcsec, and detect six ofthem with the Australian Long Baseline Array. We determine their linear sizes,and model their radio spectra using Synchrotron Self Absorption (SSA) and FreeFree Absorption (FFA) models. We derive statistical model ages, based on afitted scaling relation, and spectral ages, based on the radio spectrum, whichare generally consistent with the hypothesis that GPS and CSS sources are youngand evolving. We resolve the morphology of one CSS source with a radioluminosity of $10^{25}~\mbox{W Hz}^{-1}$, and find what appear to be twohotspots spanning 1.7 kpc. We find that our sources follow the turnover-linearsize relation, and that both homogenous SSA and an inhomogeneous FFA model canaccount for the spectra with observable turnovers. All but one of the FFAmodels do not require a spectral break to account for the radio spectrum, whileall but one of the alternative SSA and power law models do require a spectralbreak to account for the radio spectrum. We conclude that our low-luminositysample is similar to brighter samples in terms of their spectral shape,turnover frequencies, linear sizes, and ages, but cannot test for a differencein morphology.

High-resolution Observations of Low-luminosity Gigahertz-Peaked Spectrum and Compact Steep Spectrum Sources