In phylogenomics, regions of low alignment reliability and high noise are typically trimmed from multiple sequence alignments before they are used in phylogenetic inference. I introduce a new trimming tool, PhyIN, which deletes regions in which a large proportion of sites (characters) have conflicting phylogenetic signal. It does not require inference of a phylogenetic tree, as it finds neighbouring characters that cannot agree on any possible tree. In phylogenomic data of ultraconserved elements (UCE), PhyIN effectively finds the boundaries between chaotic (conflicted) and orderly regions of alignments with data for only a single locus. Its ability to work on individual loci allows it to preserve discord between gene trees and species trees.