This study investigates possibility and impossibility results of the repugnant and sadistic conclusions in population ethics and economics. The repugnant conclusion says that an enormous population with very low well-being is socially better than any smaller population with sufficiently high well-being. The sadistic conclusion says that adding individuals with negative well-being to a society is socially better than adding individuals with positive well-being to it. Previous studies have often found it challenging to avoid both undesirable conclusions. However, I demonstrate that a class of acceptable social welfare orderings can easily prevent these conclusions while adhering to standard axioms, such as anonymity, strong Pareto, Pigou-Dalton transfer, and extended continuity. Nevertheless, if the avoidance requirements for the repugnant and sadistic conclusions are strengthened, it is possible to encounter new impossibility results. These results reveal essential conflicts between the independence axiom and the avoidance of the weak repugnant conclusion when evaluating well-being profiles with different populations.