The distribution of apparent misalignment between the position angle of VLBI and VLA scale jets in core-dominated radio sources shows an unexpected bimodal form with one peak close to 0-degrees and the other near 90-degrees. We find that this misalignment distribution implies that there are two populations of core-dominated radio sources. The aligned population can be explained by sources with straight VLBI jets and small, randomly oriented, intrinsic bends between parsec and kiloparsec scales. In contrast the misaligned sources must have parsec-scale jets which are curved into low-pitch (i.e., gently curving) helices. Such a geometry when combined with the selection effects due to relativistic beaming can, under certain conditions, naturally explain these orthogonal sources. Such a helical distortion might be caused either by Kelvin-Helmholtz instabilities or precession of the jet ejection axis. In order to fit the presently observed misalignment distribution the simplest such helical model requires that misaligned sources must have core bulk Lorentz factors gamma > 20 (15-degrees/zeta), where zeta is the half-cone opening angle of the helix. Observations of lobe-dominated sources suggest that zeta < 15-degrees; implying gamma > 20. Once the effects of jet curvature are taken into account, such large Lorentz factors can be made consistent with the observed proper motions provided the Hubble constant is toward the lower end of its plausible range (i.e., H-0 almost-equal-to 40 km s-1 Mpc-1). If the Hubble constant is larger, then either the jet decelerates between core and VLBI scales or the bulk flow and pattern gamma are decoupled.