By calculating the band diagrams for the distributed Bragg mirrors of vertical-cavity surface-emitting lasers (VCSELs) with triangular two-dimensional lattice of etched holes we show that true photonic bandgap (PBG) confinement is possible for TE-like polarized light. We confirm this true PBG confinement for a low-index line defect as well as for a low-index cavity mode. Such PBG-VCSELs are compatible with the VCSEL technology and do not require a complicated assembly of three-dimensional photonic crystals.