The toroidal equilibrium in reversed field pinches (RFP) is usually obtained with image currents in a conducting shell induced by an outward displacement Delta of the plasma. For tight aspect ratio a/R approximately 1/3 (a and R are the minor and major radii) as in HBTX1A the displacement is significant with Delta /a approximately 0.1-0.15 causing a reduction in plasma cross-section area, increasing the average plasma to shell distance and giving plasma wall interaction predominantly on the toroidal outside. The authors describe experiments in which a steady vertical field is used to centre the plasma (i.e. Delta =0). Centering is demonstrated by magnetic measurements with discrete and cosine coils and the radial distribution of soft X-rays. Significant reductions in plasma resistivity, radiation, wall impurities and fluctuations are obtained.