Nonlinear wave structure of small amplitude ion acoustic solitary waves is investigated in a fluid plasma model consisting of ion and nonthermal electrons. Using the standard reductive perturbation technique (RPT), the basic set of governing equations is reduced to the Korteweg-de Vries (K-dV) and linear inhomogeneous K-dV type equations for both lower and higher order perturbed potential describing the nonlinearity. Based on appropriate conditions for inclusion of higher order effects, we have derived an MK-dV and a linear inhomogeneous MK-dV type equation for the lower and higher order perturbed potential, respectively. These analyses are further extended using the renormalization technique for the inclusion of higher order nonlinear and dispersive effects. The effect of higher order correction and various parameters on the soliton characteristics is investigated and discussed. Our present theoretical results may be more relevant for nonlinear ion acoustic waves in plasmas.