In this paper, we investigate the design of pulse shaping UK filters for impulse radio ultrawideband (UWB) communications systems. The goal of the shaping is to meet an arbitrary spectrum mask, e.g., the mask mandated by the FCC for UWB emissions. Compared with classical FIR filter designs, the current problem introduces three new challenges: (1) it is minimax with quadratic constraints, (2) a single-sided distortion function is used, (3) delay positions are treated as tuning parameters. We first approach this problem by constructing a least-squares approximation to the minimax problem where the optimization over delays can be easily solved. With the LS solution serving as an initialization, nonlinear optimization techniques are employed to fine tune the solutions.