In order to pull objects towards the light source a single tractor beam inevitably needs to be strongly nonparaxial. This stringent requirement makes such a tractor beam somewhat hypothetical. Here we reveal that the cylindrical shape of dielectric particles can effectively mitigate the nonparaxiality requirements, reducing the incidence angle of the partial plane waves of the light beam down to 45 degrees and even to 30 degrees for respectively dipole and dipole-quadrupole objects. The optical pulling force attributed to the interaction of magnetic dipole and magnetic quadrupole moments of dielectric cylinders occurs due to the TE rather than TM polarization. Therefore, the polarization state of the incident beam can be utilized as an external control for switching between the pushing and pulling forces. The results have application values towards optical micromanipulation, transportation and sorting of targeted particles.