We investigate the “flux excess” effect, whereby open solar flux estimates from spacecraft increase with increasing heliocentric distance. We analyze the kinematic effect on these open solar flux estimates of large-scale longitudinal structure in the solar wind flow, with particular emphasis on correcting estimates made using data from near-Earth satellites. We show that scatter, but no net bias, is introduced by the kinematic “bunching effect” on sampling and that this is true for both compression and rarefaction regions. The observed flux excesses, as a function of heliocentric distance, are shown to be consistent with open solar flux estimates from solar magnetograms made using the potential field source surface method and are well explained by the kinematic effect of solar wind speed variations on the frozen-in heliospheric field. Applying this kinematic correction to the Omni-2 interplanetary data set shows that the open solar flux at solar minimum fell from an annual mean of 3.82 × 10¹⁶ Wb in 1987 to close to half that value (1.98 × 10¹⁶ Wb) in 2007, making the fall in the minimum value over the last two solar cycles considerably faster than the rise inferred from geomagnetic activity observations over four solar cycles in the first half of the 20th century.