We consider a system where structural polymorphism suggests the possible existence of superconductivity through the implied structural instability. SrPd2Bi2 has two polymorphs, which can be controlled by the synthesis temperature: a tetragonal form (CaBe2Ge2-type) and a monoclinic form (BaAu2Sb2-type). Although the crystallographic difference between the two forms may, at first, seem trivial, we show that tetragonal SrPd2Bi2 is superconducting at 2.0 K, whereas monoclinic SrPd2Bi2 is not. We rationalize this finding and place it in context with other 1-2-2 phases.