Domains of individual preferences for which the well-known impossibility theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. To comprehend the limitations these results imply for social choice rules, we search for the largest domains that are possible. Here, we restrict the domain of individual preferences of precisely one individual. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto-optimal and strategy-proof social choice rules. Next, we charaterize the maximal domains which allow for Maskin monotone, non-dictatorial and Pareto-optimal social choice rules.