Because the properties of horizontally-transferred genes will reflect the mutational proclivities of their donor genomes, they often show atypical compositional properties relative to native genes. Parametric methods use these discrepancies to identify bacterial genes recently acquired by horizontal transfer. However, compositional patterns of native genes vary stochastically, leaving no clear boundary between typical and atypical genes. As a result, while strongly atypical genes are readily identified as alien, genes of ambiguous character are poorly classified when a single threshold separates typical and atypical genes. This limitation affects all parametric methods that examine genes independently, and escaping it requires the use of additional genomic information. We propose that the performance of all parametric methods can be improved by using a multiple-threshold approach. First, strongly atypical alien genes and strongly typical native genes would be identified using conservative thresholds. Genes with ambiguous compositional features would then be classified by examining gene context, including the class (native or alien) of flanking genes. By including additional genomic information in a multiple-threshold framework, we observed a remarkable improvement in the performance of several popular, but algorithmically distinct, methods for alien gene detection.