In this work, the growing process of Yb-doped YAG crystals is modified to achieve stoichiometric YbAG samples with a minimum quenching of the Yb3+-fluorescence. The best samples were grown by the Czochralski technique from rhenium-crucibles under reducing atmosphere (H2+N2). The as-grown YbAG crystals are of light blue color due to Yb2+-centers. The fluorescence lifetime of Yb3+ after annealing the YbAG crystals under oxidizing atmosphere is . The non-annealed samples show strong quenching of the Yb3+-fluorescence with a lifetime of only a few tens of microseconds depending on the actual growth conditions. This strong quenching is partially attributed to the Yb2+-centers giving rise to a cooperative energy transfer process among two excited Yb3+-ions and one non-excited Yb2+-ion. Typical quenching centers in Yb:YAG crystals grown from Ir-crucibles are Fe- and Ni-impurities. Another effective quenching center in non-annealed crystals is a complex center consisting of a Si2+-ion and a charge compensating oxygen vacancy with one trapped electron (F+color center). This type of center was identified by ESR- and ENDOR-measurements.