  In this paper we derive an improved core mass function (CMF) for the Pipe
Nebula from a detailed comparison between measurements of visual extinction and
molecular-line emission. We have compiled a refined sample of 201 dense cores
toward the Pipe Nebula using a 2-dimensional threshold identification algorithm
informed by recent simulations of dense core populations. Measurements of
radial velocities using complimentary C18O (1-0) observations enable us to cull
out from this sample those 43 extinction peaks that are either not associated
with dense gas or are not physically associated with the Pipe Nebula. Moreover,
we use the derived C18O, central velocities to differentiate between single
cores with internal structure and blends of two or more physically distinct
cores, superposed along the same line-of-sight. We then are able to produce a
more robust dense core sample for future follow-up studies and a more reliable
CMF than was possible previously. We confirm earlier indications that the CMF
for the Pipe Nebula departs from a single power-law like form with a break or
knee at M ~ 2.7 +/- 1.3 Msun. Moreover, we also confirm that the CMF exhibits a
similar shape to the stellar IMF, but is scaled to higher masses by a factor of
~4.5. We interpret this difference in scaling to be a measure of the star
formation efficiency (22 +/- 8%). This supports earlier suggestions that the
stellar IMF may originate more or less directly from the CMF.
