We report experimental results on chemical waves in 1,4-cyclohexanedione Belousov-Zhabotinsky systems that obey finite bandwidth dispersion relations. Although solitary pulses and long-wavelength pulse trains are unstable, pacemakers can generate short-wavelength patterns in which fast waves periodically annihilate at the slowly expanding pattern boundary. Along these boundaries, one finds numerous traveling defects that can nucleate rotating spirals which drift outward with the island's boundary. The drift follows logarithmic spirals and can induce spiral pair annihilation.