New hollow-core geometries in modified honeycomb photonic bandgap fibers have been investigated in order to obtain high birefringence and, at the same time, to avoid the presence of surface modes. Birefringence values up to 10(-3) have been obtained in fibers which are effectively single-mode in both C and L bands, with confinement loss lower than 1 dB/km in the same wide wavelength range.