We present a new open-source algorithm, Scalpel, for sensitive and specific discovery of INDELs in exome-capture data. By combining the power of mapping and assembly, Scalpel carefully searches the de Bruijn graph for sequence paths that span each exon. A detailed repeat analysis coupled with a self-tuning k-mer strategy allows Scalpel to outperform other state-of-the-art approaches for INDEL discovery. We extensively compared Scalpel with a battery of >10000 simulated and >1000 experimentally validated INDELs against two recent algorithms: GATK HaplotypeCaller and SOAPindel. We report anomalies for these tools to detect INDELs in regions containing near-perfect repeats. We also present a large-scale application of Scalpel for detecting de novo and transmitted INDELs in 593 families from the Simons Simplex Collection. Scalpel demonstrates enhanced power to detect long (≥20bp) transmitted events, and strengthens previous reports of enrichment for de novo likely gene-disrupting INDELs in autistic children with many new candidate genes.