Expression quantitative trait locus (eQTL) analysis relates genetic variation to gene expression, and it has been shown that power to detect eQTLs is substantially increased by adjustment for measures of expression variability derived from singular value decomposition-based procedures (referred to as expression factors, or EFs). A potential downside to this approach is that power will be reduced for eQTL that are correlated with one or more EFs, but these approaches are commonly used in human eQTL studies on the assumption that this risk is low for cis (i.e. local) eQTL associations. Using two independent blood eQTL datasets, we show that this assumption is incorrect and that, in fact, 10-25% of eQTL that are significant without adjustment for EFs are no longer detected after EF adjustment. In addition, the majority of these lost eQTLs replicate in independent data, indicating that they are not spurious associations. Thus, in the ideal case, EFs would be re-estimated for each eQTL association test, as has been suggested by others; however, this is computationally infeasible for large datasets with densely imputed genotype data. We propose an alternative, buffet-style approach in which a series of EF and non-EF eQTL analyses are performed and significant eQTL discoveries are collected across these analyses. We demonstrate that standard methods to control the false discovery rate perform similarly between the single EF and buffet-style approaches, and we provide biological support for eQTL discovered by this approach in terms of immune cell-type specific enhancer enrichment in Roadmap Epigenomics and ENCODE cell lines.