  BL Lacertae is the prototype of the BL Lac class of active galactic nuclei,
exhibiting intensive activity on parsec (pc) scales, such as intense core
variability and multiple ejections of jet components. In particular, in
previous works the existence of precession motions in the pc-scale jet of BL
Lacertae has been suggested. In this work we revisit this issue, investigating
temporal changes of the observed right ascension and declination offsets of the
jet knots in terms of our relativistic jet-precession model. The seven free
parameters of our precession model were optimized via a heuristic cross-entropy
method, comparing the projected precession helix with the positions of the jet
components on the plane of the sky and imposing constraints on their maximum
and minimum superluminal velocities. Our optimized best model is compatible
with a jet having a bulk velocity of 0.9824c, which is precessing with a period
of about 12.1 yr in the observer's reference frame and changing its orientation
in relation to the line of sight between 4 and 5 degrees, approximately.
Assuming that the jet precession has its origin in a supermassive binary black
hole system, we show that the 2.3-yr periodic variation in the structural
position angle of the very-long-baseline interferometry (VLBI) core of BL
Lacertae reported by Stirling et al. is compatible with a nutation phenomenon
if the secondary black hole has a mass higher than about six times that of the
primary black hole.
