  We present a model of blazar variability that can both reproduce smooth large
polarization angle swings, and at the same time allow for the seemingly random
behaviour of synchrotron fluxes, polarization fraction and, occasionally,
$\pi$/2 polarization jumps. We associate blazar flaring activity with a jet
carrying helical magnetic fields and propagating along a variable direction
(and possibly with a changing bulk Lorentz factor). The model predicts that for
various jet trajectories (i) EVPA can experience large smooth temporal
variations while at the same time polarization fraction ($\Pi$) can be highly
variable; (ii) $\Pi \sim 0$ near sudden EVPA jumps of 90$^{\circ}$, but can
also remain constant for large, smoother EVPA swings; (iii) the total angle of
EVPA rotation can be arbitrary large; (iv) intensity I is usually maximal at
points of fastest EVPA changes, but can have a minimum. Thus, even for a
regular, deterministic motion of a steadily emitting jet the observed
properties can vary in a non-monotonic and/or seemingly stochastic way.
Intrinsic fluctuations of the emissivity will further complicated the intensity
profiles, but are expected to preserve the polarization structure.
