The formation of Criegee intermediates by ozonolysis of different species containing C=N and C=P bonds is studied computationally. Electronic structure calculations are carried out for the energetics of ozonolysis, and the lifetime of the Criegee intermediate formed is computed by transition state theory. All calculations are carried out for formation of CH2OO, the simplest Criegee intermediate. Extremely large differences are found for the lifetime of CH2OO depending on the specific C=N, C=P, and C-C precursor, due to the great variations in the exoergicity of the ozonolysis. The largest lifetimes of CH2OO are found to be up to a millisecond range for a Schiff base precursor, being orders of magnitude greater than for C-C and C=P precursors at the same conditions. The results provide insights into the role of the precursor in determining the stability of the Criegee species formed and suggest an approach for preparing Criegee intermediates of relatively long lifetimes.