Identifying the underlying model in a set of data contaminated by noise and outliers is a fundamental task in computer vision. The cost function associated with such tasks is often highly complex, hence in most cases only an approximate solution is obtained by evaluating the cost function on discrete locations in the parameter (hypothesis) space. To be successful at least one hypothesis has to be in the vicinity of the solution. Due to noise hypotheses generated by minimal subsets can be far from the underlying model, even when the samples are from the said structure. In this paper we investigate the feasibility of using higher than minimal subset sampling for hypothesis generation. Our empirical studies showed that increasing the sample size beyond minimal size ( p ), in particular up to p+2, will significantly increase the probability of generating a hypothesis closer to the true model when subsets are selected from inliers. On the other hand, the probability of selecting an all inlier sample rapidly decreases with the sample size, making direct extension of existing methods unfeasible. Hence, we propose a new computationally tractable method for robust model fitting that uses higher than minimal subsets. Here, one starts from an arbitrary hypothesis (which does not need to be in the vicinity of the solution) and moves until either a structure in data is found or the process is re-initialized. The method also has the ability to identify when the algorithm has reached a hypothesis with adequate accuracy and stops appropriately, thereby saving computational time. The experimental analysis carried out using synthetic and real data shows that the proposed method is both accurate and efficient compared to the state-of-the-art robust model fitting techniques.