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Abstract Pulsars in binary systems with strong companion winds can have the magnetopause separating their magnetosphere from the wind located well within their light cylinder. This bow-like enclosure effectively creates a waveguide that confines the pulsar’s electromagnetic fields and can significantly alter its spindown. In this paper, we study the spindown of compressed pulsar magnetospheres in such systems. We parameterize the confinement as the ratio between the equatorial position of the magnetopause (or standoff distance)R_mand the pulsar’s light cylinderR_LC. Using particle-in-cell simulations, we quantify the pulsar spindown for a range of compressions,R_m/R_LC= 1/3–1, and inclination angles,χ= 0°…90°, between magnetic and rotation axes. Our strongly confined models (R_m/R_LC= 1/3) show two distinct limits. Forχ= 0°, the spindown of a compressed pulsar magnetosphere is enhanced by approximately a factor of three compared to an isolated pulsar due to the increased number of open magnetic field lines. Conversely, forχ= 90°, the compressed pulsar spins down at less than 40% of the rate of an isolated reference pulsar due to the mismatch between the pulsar wind stripe wavelength and the waveguide size. We apply our analysis to the 2.77 s oblique rotator (χ= 60°) in the double-pulsar system PSR J0737-3039. With the numerically derived spindown estimate, we constrain its surface magnetic field toB_*≈ (7.3 ± 0.2) × 10¹¹G. We discuss the time modulation of its period derivative, the effects of compression on its braking index, and implications for the radio eclipse in PSR J0737-3039.