We report on the generation of polarization squeezing of intense, short light pulses using an asymmetric fiber-optic Sagnac interferometer. The Kerr nonlinearity of the fiber is exploited to produce independent amplitude squeezed pulses. The polarization squeezing properties of spatially overlapped amplitude squeezed and coherent states are discussed. The experimental results for a single-amplitude squeezed beam are compared to the case of two phase-matched, spatially overlapped amplitude squeezed pulses. For the latter, noise variances of $\ensuremath{-}3.4\mathrm{dB}$ below shot noise in the ${S}_{0}$ and the ${S}_{1}$ and of $\ensuremath{-}2.8\mathrm{dB}$ in the ${S}_{2}$ Stokes parameters were observed, which is comparable to the input squeezing magnitude. Polarization squeezing, that is, squeezing relative to a corresponding polarization minimum uncertainty state, was generated in ${S}_{1}.$