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tokens: for a realistic simulated pulsar. Apart from different f - and -scales, the corresponding plot for the semicoherent mismatch looks very similar. The mismatch agrees well with its metric approximation for mismatch m ≤ 0.5, which is typical: in Appendix B , we show that the highest sensitivity at given computing cost for an elliptical search is obtained with an average mismatch (see Table B1 ). Figure 3. Comparison of the coherent metric approximation to the actual mismatch, for parameters of a simulated eccentric orbit binary pulsar in 4FGL J0523.3−2527. Blue contours show the actual mismatch and red contours the metric approximation, at m = 0.25 and 0.5. The sky position parameters { n x , n y } are not shown in Figure 3 because we assume that for spider pulsars they are known to high precision from optical observations. A partially informed search for binary pulsars in elliptic orbits, without exact information about the sky position and constraints on the orbital parameters, is computationally impossible. There are too many parameter space dimensions—even for circular orbits with reasonable parameter ranges, the grid has too many points. To make a search possible, one needs tight constraints derived from optical/X-ray observations of the pulsar’s companion star. In the next section, we will discuss constraints and the search design for the probable eccentric orbit binary gamma-ray pulsar in 4FGL J0523.3−2527 (Strader et al. 2014 ; Saz Parkinson et al. 2016 ). 4.2. Search Design for Low-eccentricity Binary In this section, we discuss how to reduce the search parameter space using orbital constraints for the gamma-ray source 4FGL J0523.3−2527, presumed to be a pulsar in an eccentric binary orbit. The source is named 3FGL J0523.3−2528, 2FGL J0523.3−2530, or 1FGL J0523.5−2529 in previous LAT source catalogs. This is similar to the circular example of Section 3.2 . The gamma-ray source itself was investigated by Saz Parkinson et al. ( 2016 ) and ranked ninth highest in a list of most significant 3FGL unassociated sources predicted to be pulsars. It shows typical pulsar-like properties: the photon flux is stable over time, and the spectrum is fit by an exponential cutoff power law. The source is not in the Galactic disk, which increases the odds that it hosts an MSP. Earlier optical observations identified a likely companion and indicate an orbit with small, but not negligible, eccentricity of (Strader et al. 2014 ). In contrast to the previous paragraph, this suggests that the pulsar is a YP, because binary MSPs tend to have rather circular orbits (Phinney 1992 ). The frequency and spin-down search ranges are chosen following the logic of the previous search design (Section 3.2 ). For YPs we search f ∈ [0, 44] Hz and . For MSPs we search f ∈ [44, 1500] Hz and . The f -dimension is efficiently searched using FFTs with bandwidth f BW = 8 Hz, and the -dimension is covered by a uniformly spaced lattice. The sky position search range of the probable