How important are helical propensities in determining the conformations of globular proteins? Using the two-dimensional lattice model and two monomer types, H (hydrophobic) and P (polar), we explore both nonlocal interactions, through an HH contact energy, as developed in earlier work, and local interactions, through a helix energy, σ. By computer enumeration, the partition functions for short chains are obtained without approximation for the full range of both types of energy. When nonlocal interactions dominate, some sequences undergo coil-globule collapse to a unique native structure. When local interactions dominate, all sequences undergo helix–coil transitions. For two different conformational properties, the closest correspondence between the lattice model and proteins in the Protein Data Bank is obtained if the model local interactions are made small compared to the HH contact interaction, suggesting that helical propensities may be only weak determinants of globular protein structures in water. For some HP sequences, varying σ/ leads to additional sharp transitions (sometimes several) and to “conformational switching” between unique conformations. This behavior resembles the transitions of globular proteins in water to helical states in alcohols. In particular, comparison with experiments shows that whereas urea as a denaturant is best modeled as weakening both local and nonlocal interactions, trifluoroethanol is best modeled as mainly weakening HH interactions and slightly enhancing local helical interactions.