Single crystals of the (Hg, Pb)(Ba, Sr)(2)Ca2Cu3O8+delta or (Hg, Pb)-1((Ba:Sr))223 phase of 100-200 mum in size have been grown by a liquid-assisted solid-state recrystallization method employing an improved encapsulation technique developed for preventing the possible explosion of the fused-quartz ampoule. Strontium-rich crystals with up to 75% Sr-for-Ba substitution were successfully obtained. Based on the results of crystal morphology investigation and the identification of the polycrystalline secondary phases, a possible growth mechanism involving the formation of small amounts of a liquid phase and a layer-by-layer growth of the (Hg, Pb)-1((Ba, Sr))223 crystals is proposed. The size of the obtained crystals was found to depend on both the density of the starting mixture pellet and the amount of oxygen in the ampoule. In order to establish the actual chemical composition of the crystals ICP analysis was performed. The as-grown crystals showed a sharp superconductivity transition at T-c = 115-128 K depending on the Sr content.