Effect sizes are often used in psychology because they are crucial when determining the required sample size of a study and when interpreting the implications of a result. Recently, researchers have been encouraged to contextualize their effect sizes and determine what the smallest effect size is that yields theoretical or practical implications, also known as the smallest effect size of interest (SESOI). Having a SESOI will allow researchers to have more specific hypotheses such as whether their findings are truly meaningful (i.e., minimum-effect testing) or whether no meaningful effect exists (i.e., equivalence testing). These types of hypotheses should be reflected in power analyses to accurately determine the required sample size. Through a confidence interval focused approach and simulations, I show how to conduct power analyses for minimum-effect and equivalence testing. Moreover, I show that conducting a power analysis for the SESOI might result in inconclusive results. This confidence interval focused simulation-based power analysis can be easily adopted to different types of research areas and designs. Last, I provide recommendations on how to conduct such simulation-based power analyses.