Samples with Mg1-xDxB2.04 (D = Pt, Pd or Re) nominal compositions have been synthesised by a solid-state route. None of these doping elements can be substituted for Mg in a detectable amount and their presence in the samples has no influence on the critical temperature and on the lattice parameters of the MgB2 superconductor. Impurity phases are formed by reaction mostly with Mg. The microstructure of the Pt, Pd and Re-based phases depends on the elements. Re-rich particles with large sizes up to 8 μm form, whereas Pt- and Pd-containing impurities are finely dispersed with a particle size that does not exceed 1 μm. The field dependence of the normalised critical current density is improved when Pt, Pd or Re are present in the samples.