In the field of non-thermal plasmas, the term 'high pressure' generally refers to pressures ranging from 0.01 to 0.1 MPa. For pressures higher than 1 MPa, the behaviour of low-current electrical discharges remains a poorly explored area. However, the study and the control of such discharges can open new prospects in many application fields such as chemistry, lighting or material synthesis. This paper reports an experimental analysis of a tip-tip electrical discharge supplied with dc voltage in a pure helium atmosphere at high pressures. The electrical characteristics of the discharge are analysed for pressures ranging from 0.1 to 15 MPa, for currents ranging from 250 to 400 mA and inter-electrode gaps ranging from 0.25 to 2.5 mm.