The grand canonical ensemble Monte Carlo simulation method is used to study the structure of Lennard–Jones fluids confined between the parallel walls, formed by the (111) planes of the face-centred cubic crystal. Thin slit pores of a width allowing for the formation of only three atomic layers are considered. It is demonstrated that in the case of fluid atoms of the size compatible with the surface lattice size the structure of confined solid-like phases is very sensitive to the pore width and to the corrugation of the surface potential. In particular, it is shown that in the case of non-corrugated surface potential the condensed (three-layer) phases of square or triangular symmetry may appear, as observed by other authors. The surface potential of finite corrugation competes with the packing effects and highly stabilizes solid-like phases of triangular symmetry.