Three four-parameter potentials,UI,UII andUIII have been proposed and their accuracy has been demonstrated by finding the mean square deviation from the true RKR potential curve for 15 electronic states of 12 diatomic molecules. Their percentage average mean square deviations from RKR curve have been found to be 1.45, 1.86 and 2.89, respectively. These compare favourably with the value 2.67 for the recently suggested four-parameter potential of Wei Hua which itself yields better results than the commonly employed three-parameter potentials. The superiority of the new potentials (especially ofUI andUII has been further established by using these potentials to calculate the molecular constants αe and ωexe following Dunham’s method. The corresponding percentage average mean deviations, for αe, turn out to be 3.75, 5.13 and 15.43 and for ωexe 8.73, 17.23 and 27.49, respectively, against the respective values of 7.97 and 18.88 with Wei Hua’s four-parameter potential. Also included are the values of dissociation energy determined with these potentials and these too corroborate the better performance ofUI andUII. The relative worth of various potential functions has been further tested by carrying out numerical study of vibrational partition function (evaluated by sum over states method), entropy and thermal capacity for the ground state of 7 molecules and comparing these with the corresponding findings based on the RKR data.