  We present estimates of the confusion limit of measurements of the
Sunyaev-Zel'dovich effect (SZ) increment near its peak intensity based on Monte
Carlo simulations of sub-millimetre observations of galaxy clusters.
Specifically, we evaluate the contribution of gravitational lensing of high
redshift background sources by a target cluster to its inferred SZ signal. We
find that the background confusion limit is 0.6 mJy per beam without any
lensing. With gravitational lensing, the confusion limit increases to 0.9 mJy
per beam. Removing bright sources in the gravitationally lensed fields
decreases the confusion limit to 0.7 mJy per beam, essentially background
levels. These limits are found by removing exceptionally poor fits to the
expected SZ profile, which are due to the different structure of the SZ and
lensing angular profiles.
  We conclude that experiments designed to measure the SZ increment must have
high enough angular resolution to identify background point sources while
surveying enough of the sky to determine the SZ profile. Observations of the SZ
increment with SCUBA, which has sufficient sensitivity and resolution for the
task, should be straight forward.
