With the aim of constraining the structural properties of neutron stars and the equation of state of dense matter , we study sudden spin-ups , glitches , occurring in the Vela pulsar and in six other pulsars . We present evidence that glitches represent a self-regulating instability for which the star prepares over a waiting time . The angular momentum requirements of glitches in Vela indicate that \geq 1.4 % of the star ’ s moment of inertia drives these events . If glitches originate in the liquid of the inner crust , Vela ’ s ‘ radiation radius ’ R _ { \infty } must exceed \simeq 12 km for a mass of 1.4 M _ { \odot } . The isolated neutron star RX J18563-3754 is a promising candidate for a definitive radius measurement , and offers to further our understanding of dense matter and the origin of glitches .