We present the results of far-infrared imaging of extended regions around three bipolar preplanetary nebulae, AFGL 2688, OH 231.8+4.2, and IRAS 16342À3814, at 70 and 160 m with the MIPS instrument on the Spitzer Space Telescope. After a careful subtraction of the point-spread function of the central star from these images, we place constraints on the existence of extended shells and thus on the mass outflow rates as a function of radial distance from these stars. We find no apparent extended emission in AFGL 2688 and OH 231.8+4.2 beyond 100 00 from the central source. In the case of AFGL 2688, this result is inconsistent with a previous report of two extended dust shells made on the basis of ISO observations. We derive upper limits of 2:1 ; 10 À7 and 1:0 ; 10 À7 M yr À1 for the dust mass-loss rates of AFGL 2688 and OH 231.8, respectively, at 200 00 from each source. In contrast to these two sources, IRAS 16342À3814 does show extended emission at both wavelengths, which can be interpreted as a very large dust shell with a radius of $400 00 and a thickness of $100 00 , corresponding to 4 and 1 pc, respectively, at a distance of 2 kpc. However, this enhanced emission may also be Galactic cirrus; better azimuthal coverage is necessary for confirmation of a shell. If the extended emission is a shell, it can be modeled, with some assumptions about its dust properties, as enhanced mass outflow at a dust mass outflow rate of 1:5 ; 10 À6 M yr À1 superimposed on a steady outflow with a dust mass outflow rate of 1:5 ; 10 À7 M yr
À1. Because of the size of the possible shell, it is likely that this shell has swept up a substantial mass of interstellar gas during its expansion, so these estimates are upper limits to the stellar mass-loss rate. We find a constant color temperature of 32 K throughout the circumstellar envelope of IRAS 16342À3814, which is consistent with heating by the interstellar radiation field.