  Drift chambers operated with helium-based gas mixtures represent a common
solution for tracking charged particles keeping the material budget in the
sensitive volume to a minimum. The drawback of this solution is the worsening
of the spatial resolution due to primary ionisation fluctuations, which is a
limiting factor for high granularity drift chambers like the MEG II tracker. We
report on the measurements performed on three different prototypes of the MEG
II drift chamber aimed at determining the achievable single-hit resolution. The
prototypes were operated with helium/isobutane gas mixtures and exposed to
cosmic rays, electron beams and radioactive sources. Direct measurements of the
single hit resolution performed with an external tracker returned a value of
110 $\mu$m, consistent with the values obtained with indirect measurements
performed with the other prototypes.
