Mapping the energy surface is an important step in understanding the protein folding process. However, it requires identification of all stationary points of the system, or at least a large number of them. Locating the full set of stationary points even for Met-enkephalin is intractable by normal sampling procedures that have been proposed to search the energy surface. We have recently suggested an enhanced combinatorial sampling technique that uses mutually orthogonal Latin squares to quickly identify the complete set of low potential energy structures of a molecule. In this paper, we have used this technique to identify 1500 low potential energy structures each for Met-enkephalin and Leu-enkephalin. We have then used a clustering procedure to reduce the sample to a set of unique conformations. Some of these have been identified earlier by other computational simulations as global energy minimum structures. Others structures in the unique set have been observed in experiments, specifically X-ray crystallography. We have used the unique sets to visualize the entire potential energy landscape as two-dimensional projections and as minimum energy envelopes. The potential energy surfaces of these peptides resemble a funnel that is broader, as well as possessing a larger number of minima that are more widely separated, than the picture demonstrated generally in the past. We are able to locate the theoretical and experimental structures on this landscape. In addition, we are able to identify a set of structures that may represent intermediate steps on the folding pathway of these two peptides.