This paper identifies the special type of SSD shift and investigates restrictions in a very strong sense on a R-S decrease in risk which is the subset of SSD. We carry out its comparative static analysis for the decision maker. The risk averse decision maker, maximizing the expected value of utility , increases the optimal level of the (nonnegative) choice variable. We also discuss the properties of decision models and preferences derived from its comparative statics result. For the preferences of the decision makers, decreasing absolute risk aversion (DARA) and increasing relative risk aversion (IRRA) generally accepted as a reasonable attitude toward risk are sufficient.