We describe an observing strategy for obtaining accurate sky subtraction when observing with a long-slit spectrograph. The technique is a chopping procedure in which the telescope is sequentially moved from object to sky on short time scales (approximate to 300 s), but instead of reading out the CCD detector with each exposure, we repeatedly clock the charge on the chip in the parallel direction in a manner that produces two complete exposures (one object + sky, one sky) on each CCD frame. The background subtraction proceeds naturally by differencing these two exposures. We show that this method provides superior results to more traditional sky-subtraction methods that rely on measuring the sky brightness at the ends of the slit. We find that we can reach a V-band surface brightness of approximate to 24 mag arcsec(-2) in about 8 hours of observing time on the 2.4-meter Hiltner telescope at the Michigan-Dartmouth-MIT Observatory. We present some preliminary results obtained with this method for the stellar dynamics in the outer envelopes of three elliptical galaxies (M87, NGC 5846, and IC 1101). We use cross-correlation and Fourier quotient techniques to derive radial velocity and velocity dispersion profiles. We confirm that the velocity dispersion in the outer envelope of IC 1101 (the central galaxy in Abell 2029) rises with distance from the center of the galaxy, as noted by Dressier [APJ. 23, 659 (1979)]. (C) 1996 American Astronomical Society.