Functional connectivity (FC) maps from brain fMRI data can be derived with dual regression, a proposed alternative to traditional seed‐based FC (SFC) methods that detect temporal correlation between a predefined region (seed) and other regions in the brain. As with SFC, incorporating nuisance regressors (NR) into the dual regression must be done carefully, to prevent potential bias and insensitivity of FC estimates. Here, we explore the potentially untoward effects on dual regression that may occur when NR correlate highly with the signal of interest, using both synthetic and real fMRI data to elucidate mechanisms responsible for loss of accuracy in FC maps. Our tests suggest significantly improved accuracy in FC maps derived with dual regression when highly correlated temporal NR were omitted. Single‐map dual regression, a simplified form of dual regression that uses neither spatial nor temporal NR, offers a viable alternative whose FC maps may be more easily interpreted, and in some cases be more accurate than those derived with standard dual regression.