The local states (LS) and hypothetical scanning (HS) methods of Meirovitch enable one to calculate approximately the absolute entropy and free energy from a sample generated with any simulation procedure. These are general methods which have been applied to a wide range of systems, magnets, lattice-gas and fluid models, as well as polymers and biological macromolecules. While LS and HS are based on the same theoretical grounds, calculation of their transition probabilities (TPs) is significantly different. TPs (LS) are obtained from pure "geometrical" considerations, by counting the number of occurrence of the so-called "local states," whereas TPs (HS) depend on the interaction energy and thus become more complicated to calculate for realistic models of proteins, for example. LS is suitable for calculating the entropy of fluctuations around a well-defined structure such as the alpha helix of a peptide, where HS fails; however, HS performs very efficiently at the other extreme, for random coiled polymers with strong excluded volume interactions. In this paper we test for the first time the efficiency of LS in the flexible regime by applying it to models of self-avoiding walks (SAWs) on a square lattice. LS is found to be significantly less efficient than HS. This suggests that to efficiently treat macromolecules with variable regions of flexibility, such as crystalline polymers or protein loops (with relatively flexible side chains), methods that are hybrid of LS and HS will be more efficient than LS and HS individually. Potential hybrid methods are discussed and two methods, denoted LS1 and LS2, are applied to the SAWs models and their efficiency is studied. The present calculations shed new light on various theoretical aspects of our approach. In particular, a recently suggested best-fit procedure for increasing the accuracy of the free energy, based on the correlation between an approximate free energy and its fluctuation, is found to perform well already for relatively bad approximations. (C) 2001 American Institute of Physics.