The recently introduced Essential Dynamics sampling method is extended such that an exhaustive sampling of the available (backbone) configurational space can be achieved. From an initial Molecular Dynamics simulation an approximated definition of the essential subspace is obtained. This subspace is used to direct subsequent simulations by means of constraint forces. The method is applied to the peptide hormone guanylin, solvated in water, of which the structure was determined recently. The peptide exists in two forms and for both forms, an extensive sampling was produced. The sampling algorithm fills the available space (of the essential coordinates used in the procedure) at a rate that is approximately six to seven times larger than that for traditional Molecular Dynamics. The procedure does not cause any significant perturbation, which is indicated by the fact that free Molecular Dynamics simulations started at several places in the space defined by the Essential Dynamics sample that complete space. Moreover, analyses of the average free Molecular Dynamics step have shown that nowhere except close to the edge of the available space, there are regions where the system shows a drift in a particular direction. This result also shows that in principle, the essential subspace is a constant free energy surface, with well-defined and steep borders, in which the system moves diffusively. In addition, a comparison between two independent essential dynamics sampling runs, of one form of the peptide, shows that the obtained essential subspaces are virtually identical.