Next-generation sequencing has yet to be widely adopted for HIV. The difficulty of accurately reconstructing the consensus sequence of a quasispecies from reads (short fragments of DNA) in the presence of rapid between- and within-host evolution may have presented a barrier. In particular, mapping (aligning) reads to a reference sequence leads to biased loss of information; this bias can distort epidemiological and evolutionary conclusions. De novo assembly avoids this bias by effectively aligning the reads to themselves, producing a set of sequences called contigs. However contigs provide only a partial summary of the reads, misassembly may result in their having an incorrect structure, and no information is available at parts of the genome where contigs could not be assembled. To address these problems we developed the tool shiver to preprocess reads for quality and contamination, then map them to a reference tailored to the sample using corrected contigs supplemented with existing reference sequences. Run with two commands per sample, it can easily be used for large heterogeneous data sets. We use shiver to reconstruct the consensus sequence and minority variant information from paired-end short-read data produced with the Illumina platform, for 65 existing publicly available samples and 50 new samples. We show the systematic superiority of mapping to shiver's constructed reference over mapping the same reads to the standard reference HXB2: an average of 29 bases per sample are called differently, of which 98.5% are supported by higher coverage. We also provide a practical guide to working with imperfect contigs.