Standard dimensionless parameters cannot simultaneously represent all operation modes of a pump-turbine. They either have singularities at E=0 and multiple values in the ‘unstable’ areas, or else get singular at n=0. P. Suter (1966) introduced an alternative set of variables which avoids singularity and always remains unique-valued. This works for non-regulated pumps but not so well for regulated machines. A modification by C.S. Martin avoids distortion at low load. The present paper describes further improvements for the representation of torque, and for closed gate (where Suter’s concept does not work). The possibility to interpolate across all operation modes is likewise useful for representing other mechanical parameters of the machine. Practical application for guide vane torque and pressure pulsation data is demonstrated by examples.