Phylogenetic comparative methods (PCMs) are commonly used to study evolution and adaptation. However, frequently used PCMs for discrete traits mishandle single evolutionary transitions. They erroneously detect correlated evolution in these situations. For example, hair and mammary glands cannot be said to have evolved in a correlated fashion because each evolved only once in mammals, but a commonly used model (Pagel’s Discrete) statistically supports correlated (dependent) evolution. Using simulations, we find that rate parameter estimation, which is central for model selection, is poor in these scenarios due to small effective (evolutionary) sample sizes of independent character state change. Pagel’s Discrete model also tends to favor dependent evolution in these scenarios, in part, because it forces evolution through state combinations unobserved in the tip data. This model prohibits simultaneous dual transitions along branches. Models with underlying continuous data distributions (e.g., Threshold and GLMM) are less prone to favor correlated evolution, but are still susceptible when evolutionary sample sizes are small. We provide three general recommendations for researchers who encounter these common situations: 1) Create study designs that evaluate a priori hypotheses and maximize evolutionary sample sizes; 2) assess the suitability of evolutionary models—for discrete traits, we introduce the phylogenetic imbalance ratio; and 3) evaluate evolutionary hypotheses with a consilience of evidence from disparate fields, like biogeography and developmental biology. These recommendations are useful for investigations that employ any type of PCM.