Conformational restrictions imposed by hydrogen bond formation during protein folding are investigated by Monte Carlo simulations of a non-native-centric, two-dimensional, hydrophobic model in which the formation of favorable contacts is coupled to an effective reduction in lattice coordination. This scheme is intended to mimic the requirement that polar backbone groups of real proteins must form hydrogen bonds concomitantly to their burial inside the apolar protein core. In addition to the square lattice, with z=3 conformations per monomer, we use extensions in which diagonal step vectors are allowed, resulting in z=5 and z=7. Thermodynamics are governed by the hydrophobic energy function, according to which hydrophobic monomers tend to make contacts unspecifically while the reverse is true for hydrophilic monomers, with the additional restriction that only contacts between monomers adopting one of zh<z local conformations contribute to the energy, where zh is the number of local conformations assumed to be compatible with hydrogen bond formation. The folding transition abruptness and van't Hoff-to-calorimetric-enthalpy ratio are found to increase dramatically by this simple and physically motivated mechanism. The observed increase in folding cooperativity is correlated to an increase in the convexity of the underlying microcanonical conformational entropy as a function of energy. Preliminary simulations in three dimensions, even though using a smaller relative reduction in lattice effective coordination zh/z=4/5, display a slight increase in cooperativity for a hydrophobic model of 40 monomers and a more pronounced increase in cooperativity for a native-centric Go-model with the same native conformation, suggesting that this purely entropic effect is not an artifact of dimensionality and is likely to be of fundamental importance in the theoretical understanding of folding cooperativity.