  We present the discovery of three modestly-irradiated, roughly Neptune-mass
planets orbiting three nearby Solar-type stars. HD 42618 b has a minimum mass
of $15.4 \pm 2.4$ M$_{\oplus}$, a semi-major axis of 0.55 AU, an equilibrium
temperature of 337 K, and is the first planet discovered to orbit the solar
analogue host star, HD 42618. We also discover new planets orbiting the known
exoplanet host stars HD 164922 and HD 143761 ($\rho$ CrB). The new planet
orbiting HD 164922 has a minimum mass of $12.9 \pm 1.6$ M$_{\oplus}$ and orbits
interior to the previously known Jovian mass planet orbiting at 2.1 AU. HD
164922 c has a semi-major axis of 0.34 AU and an equilibrium temperature of 418
K. HD 143761 c orbits with a semi-major axis of 0.44 AU, has a minimum mass of
$25 \pm 2$ M$_{\oplus}$, and is the warmest of the three new planets with an
equilibrium temperature of 445 K. It orbits exterior to the previously known
warm Jupiter in the system. A transit search using space-based CoRoT data and
ground-based photometry from the Automated Photometric Telescopes (APTs) at
Fairborn Observatory failed to detect any transits, but the precise,
high-cadence APT photometry helped to disentangle planetary-reflex motion from
stellar activity. These planets were discovered as part of an ongoing radial
velocity survey of bright, nearby, chromospherically-inactive stars using the
Automated Planet Finder (APF) telescope at Lick Observatory. The high-cadence
APF data combined with nearly two decades of radial velocity data from Keck
Observatory and gives unprecedented sensitivity to both short-period low-mass,
and long-period intermediate-mass planets.
