"Sequencing by synthesis" (SBS) is a rapidly emerging high-throughput low-cost sequencing technology, and is one of the front-runners in the race to the $10,000 genome. SBS reads are currently short, approximately ranging from 30 to 100-150 bp long on different technology platforms. Shotgun sequence assembly of such short reads is complicated by the presence of repeats, and this presents a major obstacle to use SBS for de novo sequencing of large genomes and of genomes having significant amounts of repetitive sequence. Here we propose using a radical technique called "sequencing aided by mutagenesis" (SAM) to solve many aspects of this problem. The technique involves deliberately introducing mutations into the target DNA to reduce its repetitiveness, assembling sequences of several such mutants and then inferring the target sequence from the assembled mutant sequences. We present the results of simulation SAM reassemblies of different human genomic fragments and motifs up to 600 kb long, as well as of the entire Mycoplasma genitalium genome. Each of these fragments could be successfully reconstructed from short reads of lengths 25, 100 or 150 bp using Phrap, demonstrating the potential of SAM as an enabling technology for short-read sequencing output.