  We present the results of far-infrared imaging of extended regions around
three bipolar pre-planetary nebulae, AFGL 2688, OH 231.8+4.2, and IRAS
16342$-$3814, at 70 and 160 $\mu$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 arcseconds 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 an upper limit of
$2.1\times10^{-7}$ M$_\odot$ yr$^{-1}$ and $1.0\times10^{-7}$ M$_\odot$
yr$^{-1}$ for the dust mass loss rate of AFGL 2688 and OH 231.8, respectively,
at 200 arcseconds from each source. In contrast to these two sources, IRAS
16342$-$3814 does show extended emission at both wavelengths, which can be
interpreted as a very large dust shell with a radius of $\sim$ 400 arcseconds
and a thickness of $\sim$ 100 arcseconds, corresponding to 4 pc 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 as enhanced
mass outflow at a dust mass outflow rate of $1.5\times10^{-6}$ M$_\odot$
yr$^{-1}$ superimposed on a steady outflow with a dust mass outflow rate of
$1.5\times10^{-7}$ M$_\odot$ yr$^{-1}$. 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.
