We present the results of an all-sky search for continuous gravitational-wave signals with frequencies in the 500-1700 Hz range targeting neutron stars with ellipticity of 10-8. The search is done on LIGO O2 data using the Falcon analysis pipeline. The results presented here double the sensitivity over any other result on the same data [B. P. Abbott (LIGO Scientific Collaboration and Virgo Collaboration), Phys. Rev. D 100, 024004 (2019)PRVDAQ2470-001010.1103/PhysRevD.100.024004, C. Palomba, Phys. Rev. Lett. 123, 171101 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.171101]. The search is capable of detecting low-ellipticity sources up to 170 pc. We establish strict upper limits which hold for worst-case signal parameters. We list outliers uncovered by the search, including several which we cannot associate with any known instrumental cause. © 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.