We present a detailed characterization of passive, picosecond optical-power-limiting devices using tightly focused beams in thick semiconductor samples. This study of limiting in ZnSe with 30-psec, 532-nm pulses shows that the resulting internal self-action (two-photon absorption plus free-carrier self-defocusing) protects the bulk material from optical damage. Simple scaling relations were determined from our results that link the limiting energy and the dynamic range to the focusing geometry and sample dimensions. These relations were used to design a monolithic optical limiter, optimized to have maximum dynamic range and minimum limiting energy. This device limits at an input energy of 10 nJ (300 W) and has a dynamic range greater than 10(4).