  Continuous gravitational waves represent one of the long-sought types of
signals that have yet to be detected. Due to their small amplitude, long
observational datasets (months-years) have to be analyzed together, thereby
vastly increasing the computational cost of these searches. All-sky searches
face the most severe computational obstacles, especially searches for sources
in unknown binary systems, which need to break the data into very short
segments in order to be computationally feasible. In this paper, we present a
new detection statistic that improves sensitivity by up to 19% compared to the
standard $\mathcal{F}$-statistic for segments shorter than a few hours.
