The invention provides methods and compositions for attaching oligonucleotide tags to polynucleotides for the purpose of carrying out analytical assays in parallel and for decoding the oligonucleotide tags of polynucleotides selected in such assays. Words, or subunits, of oligonucleotide tags index submixtues in successively more complex sets of submixtures (referred to herein as “tiers” of submixtures) that a polynucleotide goes through while successive words are added to a growing tag. By identifying each word of an oligonucleotide tag, a series of submixtures is identified including the first submixture that contains only a single polynucleotide, thereby providing the identity of the selected polynucleotide. The analysis of the words of an oligonucleotide tag can be carried out in parallel, e.g. by specific hybridization of the oligonucleotide tag to its tag complement on an addressable array; or such analysis can be carried out serially by successive specific hybridizations of labeled word complements, or the like.