Eight mechanisms that have been proposed to account for the timing noise process in isolated pulsars are analyzed quantitatively. Of these, it is found that five face severe difficulties in meeting the observations. These are the notions that timing noise arises from: (1) starquakes; (2) the random pinning and unpinning of vortex lines (hard superfluidity); (3) accretion from the interstellar medium; (4) vortex annihilation at the outer boundary of the superfluid; and (5) pulse-shape changes. The remaining three mechanisms are found to be severely constrained, although not ruled out, by the observations. These are the notions that pulsar timing noise arises from: (6) crust breaking by vortex pinning; (7) the response of the star to a series of heat pulses; and (8) luminosity-related torque fluctuations.