The timing properties of radio pulsars provide a unique probe of neutron star interiors. Recent observations have uncovered quasiperiodicities in the timing and pulse properties of some pulsars, a phenomenon that has often been attributed to free precession of the neutron star, with profound implications for the distribution of superfluidity and superconductivity in the star. We advance this program by developing consistency relations between free precession and pulsars glitches, and we show that there are difficulties in reconciling the two phenomena in some precession candidates. This indicates that the precession model used here needs to be modified or some other phenomenon is at work in producing the quasiperiodicities, or even that there is something missing in terms of our understanding of glitches. © 2017 Authors.