The sustainment of ultra-low-q (ULQ) and reversed field pinch (RFP) discharges longer than the vertical field penetration time constant of the shell in the HBTX-IC device reveals new unstable modes arising from resistive shell instabilities. Their suppression in ULQ discharges has been achieved by controlling the value of the edge safety factor qa. The qa boundary or current limitation often seen in low-q tokamak and ULQ plasmas is found to be related to a resonant mode with a growth rate that is fast compared to the vertical field time constant of the shell. The interaction of these two types of unstable modes results in stepwise plasma current behaviour in ULQ discharges. The resistivity anomaly in ULQ discharges is larger than that in RFP discharges and can be interpreted in terms of the low density and rapid particle recycling. Different plasma relaxation phenomena are observed in these regimes.