We propose two new concepts of second-degree stochastic dominance (SSD) shifts, ‘the extended strong SSD (ESSSD) shift’ and ‘the left-side extended strong SSD (L-ESSSD) shift’ to obtain the desired comparative statics results and explore some properties of these ones. The ESSSD order can be decomposed into the monotone probability ratio (MPR) and the extended strong increases in risk (ESIR) one, and the L-ESSSD shift can be decomposed into the MPR and the left-side extended strong increases in risk (L-ESIR) one. Note that the ESSSD shift is the subset of the L-ESSSD one. One can obtain the appealing comparative statics results for these shifts given risk-averse decision makers who are prudent.