Genome copy number is an important source of genetic variation in health and disease. In cancer, Copy Number Alterations (CNAs) can be inferred from short-read sequencing data, enabling genomics-based precision oncology. Emerging Nanopore sequencing technologies offer the potential for broader clinical utility, for example in smaller hospitals, due to lower instrument cost, higher portability, and ease of use. Nonetheless, Nanopore sequencing devices are limited in the number of retrievable sequencing reads/molecules compared to short-read sequencing platforms, limiting CNA inference accuracy. To address this limitation, we targeted the sequencing of short-length DNA molecules loaded at optimized concentration in an effort to increase sequence read/molecule yield from a single nanopore run. We show that short-molecule nanopore sequencing reproducibly returns high read counts and allows high quality CNA inference. We demonstrate the clinical relevance of this approach by accurately inferring CNAs in acute myeloid leukemia samples. The data shows that, compared to traditional approaches such as chromosome analysis/cytogenetics, short molecule nanopore sequencing returns more sensitive, accurate copy number information in a cost effective and expeditious manner, including for multiplex samples. Our results provide a framework for short-molecule nanopore sequencing with applications in research and medicine, which includes but is not limited to, CNAs.