The H-mode, an improved confinement regime, was attained recently in JIPP T-IIU high power heating experiments, in a limiter configuration without any shaping of the plasma cross-section. This H-mode is unusual because it was obtained with heating in the ion cyclotron range of frequencies (ICRF). It was also attained with combined ICRF and neutral beam injection (NBI) heating. The threshold power level obtained with ICRF alone is similar to or less than that obtained in the combined heating case. The dependence of the power threshold of the H-mode on various plasma parameters has been studied. It increases with the plasma current and is insensitive to the plasma density, and there is an optimum value of the toroidal field intensity. The power deposition profile for ICRF heating has been analysed with a ray tracing code and used to explain the observed dependence on the toroidal magnetic field. The paper also discusses a class of discharges with improved confinement observed in the same series of experiments. These discharges had a power level close to the H-mode threshold power and exhibited a marked improvement of confinement. They were, however, different from H-mode discharges in the time evolution of the profiles.