Two types of improved confinement regime, H-mode and IOC (improved Ohmic confinement) mode, are studied in circular limiter plasmas on JIPP T-IIU. When rapid ramp-down of plasma current (CRD) is used during auxiliary heating, the threshold heating power required for the L-H transition is reduced by 30-50%, compared with that in the case without CRD. This is interpreted as being due to enhancement of the global magnetic shear near the plasma edge by CRD. This model, based on edge magnetic shear is also applicable to the limiter H-mode obtained without CRD by high heating power. In the limiter configuration, the IOC-mode is obtained in ohmically heated, high density plasmas by gas puff control. This improvement may be attributed to a reduction of anomalous transport since radiation loss has only a minor effect.