In this paper, we present a novel frequency-selective surface (FSS) design aimed at enhancing the performance of broad-band reconfigurable antenna apertures. In particular, reconfigurable printed dipole arrays are examined in the presence of a multilayer FSS. Of particular interest is the design of FSS structures whose reflection coefficient has prespecified phase response over a broad set of frequencies. Previous FSSs primarily considered designs on the basis of the reflection-coefficient amplitude and were intended for radome applications rather than substrates. Designing FSSs subject to phase requirements will be seen to require some compromise in the magnitude. Broad-band requirements also present us with a need for noncommensurate FSS designs.