In a cation exchange process developed recently by some of us, epitaxial HgBa2CaCu2O6 films can be obtained by diffusing volatile Tl cations out of, and simultaneously diffusing Hg cations into, the crystalline lattice of epitaxial Tl2Ba2CaCu2O8 (Tl-2212) precursor films. When a large number of Tl cations diffuse out from the same local area of the precursor lattice simultaneously, it causes lattice collapse locally and leads to formation of pores of micrometer dimension. To eliminate such large-scale lattice collapse, “lattice pins” were introduced on the original Tl-2212 lattice by partially replacing volatile Tl cations with nonvolatile Re ones. Since the Re cations remain on the lattice during the Tl-Hg cation exchange, they pin the lattice around them. HgBa2CaCu2O6 films obtained from these Re-doped Tl-2212 precursor films have much improved microstructures with the pore dimension reduced by an order of magnitude.