Coupling of core modes to surface modes in an air-core photonic-bandgap fiber (PBF) can cause large propagation losses. Computer simulations analyze the relationship between the geometry and the presence of surface modes in PBFs having a triangular hole pattern and identify ranges of core characteristic dimensions (e.g., radii) for which the fiber supports no surface modes (i.e., only core modes are present) over the entire wavelength range of the bandgap. In particular, for a hole spacing Λ and a hole radius ρ=0.47Λ, the core supports a single mode and supports no surface modes for core radii between about 0.68Λ and about 1.05Λ. The existence of surface modes can be predicted simply and expediently by studying either the bulk modes alone or the geometry of the fiber without requiring a full analysis of the defect modes.