In this paper, we point out some practical obstacles arising in realization of compressional optical coherence elastography (OCE) that have not attracted su±cient attention previously. Specifically, we discuss (i) complications in quantification of the Young modulus of tissues related to partial adhesion between the OCE probe and soft intervening reference layer sensor, (ii) distorting influence of tissue surface curvature/corrugation on the subsurface strain distribution mapping, (iii) ways of signal-to-noise ratio (SNR) enhancement in OCE strain mapping when periodic averaging is not realized, and (iv) potentially significant influence of tissue elastic nonlinearity on quantification of its stiffness. Potential practical approaches to mitigate the effects of these complications are also described.