Studies of the genetic loci that contribute to variation in geneexpression frequently identify eQTL with broad effect on geneexpression: trans-eQTL hot spots. We have developed a set of exploratory as well as formal statistical methods for assessing whether a given hotspot is due to one or multiple polymorphisms, and to define the QTL interval in the case that it appears to be due to a single polymorphism. A useful device is to examine the pattern of gene expression, in the genes that map to a given trans-eQTL hotspot, among individuals that show no recombination event in the region, in comparison to individuals that did have a recombination event. The QTL effects, including the degree of dominance, can also be informative. As part of our formal test for one vs two polymorphismsin a region, we consider a two-QTL model with each expression trait affected by one or the other QTL.