A generic cardiomyocyte ionic model, whose complexity lies between a simple phenomenological formulation and a biophysically detailed ionic membrane current description, is presented. The model provides a user-defined number of ionic currents, employing two-gate Hodgkin-Huxley type kinetics. Its generic nature allows accurate reconstruction of action potential waveforms recorded experimentally from a range of cardiac myocytes. Using a multiobjective optimisation approach, the generic ionic model was optimised to accurately reproduce multiple action potential waveforms recorded from central and peripheral sinoatrial nodes and right atrial and left atrial myocytes from rabbit cardiac tissue preparations, under different electrical stimulus protocols and pharmacological conditions. When fitted simultaneously to multiple datasets, the time course of several physiologically realistic ionic currents could be reconstructed. Model behaviours tend to be well identified when extra experimental information is incorporated into the optimisation.