A data storage medium for perpendicular recording has a substrate and a ferromagnetic layer on the substrate for storing data bits. The ferromagnetic layer has a plurality of elongate grains of magnetizable material extending perpendicular to the substrate which form magnetic domains representative of data. Each magnetic domain is separated from adjacent magnetic domains by a bit edge domain wall region. Each elongate grain has a perpendicular height that is greater than a width of the bit edge domain wall region.