MOTIVATION: Accurate alignments between entire genomes are crucial for comparative genomics. However, computing sensitive and accurate genome alignments is a challenging problem, complicated by genomic rearrangements. RESULTS: Here we present a fast approach, called chainCleaner, that improves the specificity in genome alignments by accurately detecting and removing local alignments that obscure the evolutionary history of genomic rearrangements. Systematic tests on alignments between the human and other vertebrate genomes show that chainCleaner (i) improves the alignment of numerous orthologous genes, (ii) exposes alignments between exons of orthologous genes that were masked before by alignments to pseudogenes, and (iii) recovers hundreds of kilobases in local alignments that otherwise would fall below a minimum score threshold. Our approach has broad applicability to improve the sensitivity and specificity of genome alignments. AVAILABILITY AND IMPLEMENTATION: http://bds.mpi-cbg.de/hillerlab/chainCleaner/ or https://github.com/ucscGenomeBrowser/kent. CONTACT: [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.