Eu2+ doped SrI2 is an important scintillator having applications in the field of radiation detection. Codoping techniques are often useful to improve the electronic response of such insulators. Using first-principles based approach, we report on the properties of SrI2:Eu and the influence of codoping with aliovalent (Na, Cs) and isovalent (Mg, Ca, Ba, and Sn) impurities. These codopants do not preferably bind with Eu and are expected to remain as isolated impurities in the SrI2 host. As isolated defects they display amphoteric behavior having, in most cases, significant ionization energies of the donor and acceptor levels. Furthermore, the acceptor states of Na, Cs, and Mg can bind with I-vacancy forming charge compensated donor-acceptor pairs. Such pairs may also bind additional holes or electrons similar to the isolated defects. Lack of deep-to-shallow behavior upon codoping and its ramifications will be discussed.