  We present a modification to the iodine cell Doppler technique that
eliminates the need for an observed stellar template spectrum. For a given
target star, we iterate toward a synthetic template spectrum beginning with an
existing spectrum of a similar star. We then perturb the shape of this
first-guess template to match the program observation of the target star taken
through an iodine cell. The elimination of a separate template observation
saves valuable telescope time, a feature that is ideally suited for the
quick-look strategy employed by the ``Next 2000 Stars'' (N2K) planet search
program. Tests using Keck/HIRES spectra indicate that synthetic templates yield
a short-term precision of 3 m/s and a long-term, run-to-run precision of 5 m/s.
We used this new Doppler technique to discover three new planets: a 1.5 Mjup
planet in a 2.1375 d orbit around HD 86081; a 0.71 Mjup planet in circular,
26.73 d orbit around HD 224693; and a Saturn-mass planet in an 18.179 d orbit
around HD 33283. The remarkably short period of HD 86081b bridges the gap
between the extremely short-period planets detected in the OGLE survey and the
16 Doppler-detected hot jupiters (P < 15 d), which have an orbital period
distribution that piles up at about three days. We have acquired photometric
observations of two of the planetary host stars with the automated photometric
telescopes at Fairborn Observatory. HD 86081 and HD 224693 both lack detectable
brightness variability on their radial velocity periods, supporting
planetary-reflex motion as the cause of the radial velocity variability. HD
86081 shows no evidence of planetary transits in spite of a 17.6% transit
probability.
