We report pulsed squeezed-light generation by means of an optical parametric downconverter that is pumped by the second harmonic of a mode-locked Q-switched laser. Using the fundamental beam of the laser as a local oscillator, we observe 2-dB squeezing for a parametric gain of 2.0. This local oscillator, however, is nonoptimal because of its spatiotemporal mode mismatch with the squeezed mode generated by the downconverter. We describe an experiment in which a matched local oscillator is generated with the use of an optical parametric amplifier that is pumped by the same laser as is the downconverter. In this case, 2-dB squeezing is observed for a parametric gain of 1.5. The present experimental setup is limited by uncontrollable phase fluctuations that prohibit us from making squeezing measurements at higher gains.