  The detection of unpulsed TeV emission from PSR B1706-44 raised the question
if this VHE emission results from inverse Compton scattering of multi-TeV
electrons on the CMBR and other soft photon fields. This hints at the existence
of an unseen synchrotron nebula, which is larger than the observed 1 arcminute
compact X-ray nebula. In a search for synchrotron counterpart of the TeV
nebula, we have taken V-band CCD images of the region around the PSR B1706-44
pulsar position. By rejecting all point source contributions down to the
diffuse sky limit, we were able to search for such extended plerionic
synchrotron emission on scale sizes limited by the angular resolution of the
CANGAROO imaging TeV observations. By combining the V-band flux limits with the
observed TeV flux, we were able to obtain upper limits for the magnetic field
strength as a function of the radius of the assumed TeV nebula. Assuming that
the 2 arcminute radio plerion also defines the size of the TeV nebula, we
constrain the steady state particle spectral index to the values between 4 and
5.5, with a field strength limit of about 3x10^-6 G. This compares with an
index of 3.6+/-0.6 inside the 1 arcminute compact X-ray nebula.
