Context. The study of old, metal-poor stars deepens our knowledge on the early stages of the universe. In particular, the study of these stars gives us a valuable insight into the masses of the first massive stars and their emission of ionising photons. Aims. We present a detailed chemical analysis and determination of the kinematic and orbital properties of a sample of 11 dwarf stars. These are metal-poor stars, and a few of them present a low lithium content. We inspected whether the other elements also present anomalies. Methods. We analysed the high-resolution UVES spectra of a few metal-poor stars using the Turbospectrum code to synthesise spectral lines profiles. This allowed us to derive a detailed chemical analysis of Fe, C, Li, Na, Mg, Al, Si, CaI, CaII, ScII, TiII, Cr, Mn, Co, Ni, Sr, and Ba. Results. We find excellent coherence with the reference metal-poor First Stars sample. The lithium-poor stars do not present any anomaly of the abundance of the elements other than lithium. Among the Li-poor stars, we show that CS 22882-027 is very probably a blue-straggler. The star CS 30302-145, which has a Li abundance compatible with the plateau, has a very low Si abundance and a high Mn abundance. In many aspects, it is similar to the α-poor star HE 1424-0241, but it is less extreme. It could have been formed in a satellite galaxy and later been accreted by our Galaxy. This hypothesis is also supported by its kinematics.