A theoretical investigation is carried out to understand the basic features of ion-acoustic (IA) waves in an unmagnetised plasmas including cool ions, hot ions having a kappa distribution and kappa-distributed electrons, using small amplitude techniques. The effects of excess suprathermal ions, the ion temperature Ti and electron temperature Te as well as the density ratio on the IA waves are studied. It is found that the suprathermality effects play an important role in the system, as the geometric characteristics of the IA solitons are found to be significantly affected through the ion and electron suprathermal index. In the presence of suprathermality effects, either polarity is in principle supported by this plasma model.