Light transmission through complex-unit waveguides (WGs) with or without stubs attached to them periodically is studied theoretically. The transmittance through stubless WGs of width a, with periodic dielectric contrast and two different subunits, exhibits longitudinal resonances due to bound states trapped in individual subunits that disappear when the optical lengths of the latter are sufficiently long. On the other hand, stubbed WGs can have bound states trapped in the stubs which may result in transmittance resonances in the gaps and antiresonances within the bands that can widen into new bands and gaps, respectively. The photonic gaps of the stubbed WGs, with or without dielectric contrast, can be several times larger than those of the corresponding one-dimensional quarter-wave structure for sufficiently short a. This increase results from destructive interference between waves propagating along the main WG and those reflected from the stubs. Distributedfeedback-laser stubbed or stubless (with contrast) structures, of stub length s โ a, show a much higher Q than that of conventional, weakly corrugated WGs.