  Context. In recent years, the R-Process Alliance (RPA) has conducted a
successful search for stars enhanced in elements produced by the rapid
neutron-capture (r-)process. In particular, the RPA has uncovered a number of
stars strongly enriched in light r-process elements, such as Sr, Y and Zr, the
so-called limited-r stars, in order to investigate the astrophysical production
site(s) of these elements. Aims. With this paper, we aim to investigate the
possible formation sites for light neutron-capture elements, by deriving
detailed abundances for neutron-capture elements from high-resolution, high
signal-to-noise spectra of three limited-r stars. Methods. We conducted a 1D
local thermodynamic equilibrium spectroscopic abundance analysis of three
stars, as well as a kinematic analysis. Further, we calculated the lanthanide
mass fraction (XLa) of our stars and of limited-r stars from the literature.
Results. We found that the neutron-capture element abundance pattern of
limited-r stars behaves differently depending on their [Ba/Eu]] ratios, and
suggest that this should be taken into account in future investigations of
their abundances. Furthermore, we found that the XLa of limited-r stars is
lower than that of the kilonova AT2017gfo. The latter seems to be in the
transition zone between limited-r XLa and that of r-I, r-II stars. Finally, we
found that, unlike r-I and r-II stars, the current sample of limited-r stars
are largely born in the Galaxy rather than being accreted.
