Methods are provided for efficient shotgun sequencing to allow efficient selection and sequencing of nucleic acids of interest contained in a library. The nucleic acids of interest can be defined any time before or after preparation of the library. One example of nucleic acids of interest is missing or low confidence genome sequences resulting from an initial sequencing procedure. Other nucleic acids of interest include subsets of genomic DNA, RNA or cDNAs (exons, genes, gene sets, transciptomes). By designing an efficient (simple to implement, speedy, high specificity, low cost) selection procedure, a more complete sequence is achieved with less effort than by using highly redundant shotgun sequencing in an initial sequencing procedure