The disclosed embodiments concern methods, systems and computer program products for determining sequences of interest using unique molecular indexes (UMIs) that are uniquely associable with individual polynucleotide fragments, including sequences with low allele frequencies or long sequence length. In some implementations, the UMIs include variable-length nonrandom UMIs (vNRUMIs). Methods and systems for making and using sequencing adapters comprising vNRUMIs are also provided.