The effect of tertiary interactions on the observed secondary structure found in the native conformation of globular proteins was examined in the context of a reduced protein model. Short-range interactions are controlled by knowledge based statistical potentials that reflect local conformational regularities seen in a; database of three-dimensional protein structures. Long-range interactions are approximated by mean field, single residue based, centrosymmetric hydrophobic burial potentials. Even when pairwise specific long-range interactions are ignored, the inclusion of such burial preferences noticeably modifies the equilibrium chain conformations, and the observed secondary structure is closer to that seen in the folded state. For a test set of 10 proteins (belonging to various structural classes), the accuracy of secondary structure prediction is about 66% and increases by 9% with respect to a related model based on short-range interactions alone [Kolinski et al., J. Chem. Phys. 103, 4312 (1995)]. The increased accuracy is due to the interplay between the short-range conformational propensities and the burial and compactness requirements built into the present model. While the absolute level of accuracy assessed on a per residue basis is comparable to more standard techniques, in contrast to these approaches, the conformation of the chain now has a better defined geometric context. For example, the assumed spherical domain protein model that simulates the segregation of residues between the hydrophobic core and the hydrophilic surface allows for the prediction of surface loops/turns where the polypeptide chain changes its direction. The implications of having such self-consistent secondary structure predictions for the prediction of protein tertiary structure are briefly discussed.