Energy minigaps caused by lateral-surface structures in quasi-one-dimensional quantum well wires are calculated using the variational and degenerate-perturbational approaches for GaAs/AlAs wires. By a coordinate transformation, the structured interfaces of the wires are transformed into planar ones so that the boundary conditions of the electronic wave functions can be satisfied exactly on the interfaces. The dependences of the energy minigaps on the lateral-surface structures are discussed.