High performance discharges with optimised magnetic shear having a broad or hollow current density profile have been produced in JET. These plasmas are characterised by improved core confinement within a region called the Internal Transport Barrier (ITB). Near the plasma centre, the ion thermal diffusivity is reduced to levels close to the standard neo-classical level in both D-D and D-T plasmas. With D-D fuel, a JET record neutron yield (RNT = 5.6x1016 s-1) was produced and, with D-T fuel, L-mode discharges with 7.2MW of fusion power, and H-mode discharges with up to 8.2MW of fusion power are obtained. Central ion temperatures approaching 40keV, ion temperature gradients of 150keVm-1 and plasma pressure gradients of 106Pam-1 are observed in DT leading to a fusion triple product niTiτE = (1.1 ± 0.2) x1021 m-3 keVs. Central toroidal rotation frequencies up to 37kHz are observed and the rotational flow near the radius of the ITB is strongly sheared. These plasmas are prepared by applying Lower Hybrid Current Drive (LHCD) and Ion Cyclotron Resonance Heating (ICRH) during the early current ramp-up phase, "freezing-in" a flat or possibly slightly hollow current density profile; into this target the main heating, consisting of combined Neutral Beam Injection (NBI) and ICRH, is applied. By superposing an ITB with an edge barrier (ELMy H-mode), near steady-state conditions (H-89 ≈ 2 for four energy confinement times) with high fusion yield have been achieved, offering a possible route towards quasi-steady-state. High fusion yield, quasi-steady-state plasmas with confinement significantly above the standard sawtoothing ELMy H-mode can be achieved in this way. The techniques previously developed with D-D plasmas were modified to allow an L-mode ITB to form in D-T with a lower L to H-mode power threshold. The heating power and the q-profile were similar in both cases. ICRH plays a key role in the direct heating of core ions which allows real-time control of the central pressure profile.