Genetic disorders can be detected by prenatal diagnosis using Chorionic Villus Sampling, but the 1:100 chance to result in miscarriage restricts the use to fetuses that are suspected to have an aberration. Detection of trisomy 21 cases noninvasively is now possible owing to the upswing of next-generation sequencing (NGS) because a small percentage of fetal DNA is present in maternal plasma. However, detecting other trisomies and smaller aberrations can only be realized using high-coverage NGS, making it too expensive for routine practice. We present a method, WISECONDOR (WIthin-SamplE COpy Number aberration DetectOR), which detects small aberrations using low-coverage NGS. The increased detection resolution was achieved by comparing read counts within the tested sample of each genomic region with regions on other chromosomes that behave similarly in control samples. This within-sample comparison avoids the need to re-sequence control samples. WISECONDOR correctly identified all T13, T18 and T21 cases while coverages were as low as 0.15-1.66. No false positives were identified. Moreover, WISECONDOR also identified smaller aberrations, down to 20 Mb, such as del(13)(q12.3q14.3), +i(12)(p10) and i(18)(q10). This shows that prevalent fetal copy number aberrations can be detected accurately and affordably by shallow sequencing maternal plasma. WISECONDOR is available at bioinformatics.tudelft.nl/wisecondor.