The generation of femtosecond Kalpha x rays from laser-irradiated plasmas is studied with a view to optimizing photon number and pulse duration. Using analytical and numerical models of hot electron generation and subsequent transport in a range of materials, it is shown that an optimum laser intensity I(opt) = 7x10(9)Z4.4 exists for maximum Kalpha yield. Furthermore, it is demonstrated that bulk targets are unsuitable for generating sub-ps x-ray pulses: instead, design criteria are proposed for achieving Kalpha pulse durations </=100 fs using foils of approximately 2 &mgr;m thickness.