The method involves growing a boule of co-doped LYSO:Ce,Ca scintillation crystal containing Ce3+ ions and Ce4+ ions in a ratio of about 1:1, wherein the grown boule is substantially free of Li+ ions and Mg2+ ions. This is achieved by providing a specialized crystal growing device having an inner iridium crucible and loading it with specific oxides and a carbonate salt in specific amounts. The loaded iridium crucible is then subjected to a vacuum and then pressurized with a specific gas mixture consisting mostly of Ar admixed with a small amount of CO. The loaded and pressurized iridium crucible is then heated to yield a melt, into which a seed crystal is placed to grow (by way of the Czochrolaski pull method) an unfinished crystalline boule. This unfinished boule is then annealed in the same special pressurized atmosphere to yield the final boule of co-doped LYSO:Ce, Ca scintillation crystal.