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Context.In recent years, theR-Process Alliance (RPA) has conducted a successful search for stars that are enhanced in elements produced by the rapid neutron-capture (r-)process. In particular, the RPA has uncovered a number of stars that are strongly enriched in lightr-process elements, such as Sr, Y, and Zr. These so-called limited-rstars were investigated to explore the astrophysical production site(s) of these elements. Aims.We investigate the possible formation sites for light neutron-capture elements by deriving detailed abundances for neutron-capture elements from high-resolution spectra with a high signal-to-noise ratio of three limited-rstars. Methods.We conducted a kinematic analysis and a 1D local thermodynamic equilibrium spectroscopic abundance analysis of three stars. Furthermore, we calculated the lanthanide mass fraction (X_La) of our stars and of limited-rstars from the literature. Results.We found that the abundance pattern of neutron-capture elements of limited-rstars behaves differently depending on their [Ba/Eu] ratios, and we suggest that this should be taken into account in future investigations of their abundances. Furthermore, we found that theX_Laof limited-rstars is lower than that of the kilonova AT2017gfo. The latter seems to be in the transition zone between limited-rX_Laand that ofr-I andr-II stars. Finally, we found that unliker-I andr-II stars, the current sample of limited-rstars is largely born in the Galaxy and is not accreted.