  Analysis of new precision radial velocity (RV) measurements from the Lick
Automated Planet Finder (APF) and Keck HIRES have yielded the discovery of
three new exoplanet candidates orbiting two nearby K dwarfs not previously
reported to have companions (HD 190007 & HD 216520). We also report new
velocities from both the APF and the Planet Finder Spectrograph (PFS) for the
previously reported planet host stars GJ 686 and HD 180617 and update the
corresponding exoplanet orbital models. Of the newly discovered planets, HD
190007 b has a period of 11.72 days, an RV semi-amplitude of K = 5.64$\pm$0.55
m s$^{-1}$, a minimum mass of 16.46$\pm$1.66 $\rm M_{\oplus}$, and orbits the
slightly metal-rich, active K4 dwarf star HD 190007 (d = 12.7 pc). HD 216520 b
has an orbital period of 35.45 days, an RV semi-amplitude of K = 2.28$\pm$0.20
m s$^{-1}$, and a minimum mass of 10.26$\pm$0.99 $\rm M_{\oplus}$, while HD
216520 c has an orbital period of P = 154.43 days, an RV semi-amplitude of K =
1.29$\pm0.22$ m s$^{-1}$, and a minimum mass of 9.44$\pm$1.63 $\rm M_{\oplus}$.
Both of these planets orbit the slightly metal-poor, inactive K0 dwarf star HD
216520 (d = 19.6 pc). We find that our updated best fit models for HD 180617 b
and GJ 686 b are in good agreement with the previously published results. For
HD 180617 b we obtain an orbital period of 105.91 days, an RV semi-amplitude of
K = 2.696$\pm$0.22 m s$^{-1}$, and a minimum mass of 2.214$\pm$1.05 $\rm
M_{\oplus}$. For GJ 686 b we find the orbital period to be 15.53 days, the RV
semi-amplitude to be K = 3.00$\pm$0.18 m s$^{-1}$, and the minimum mass to be
6.624$\pm$0.432 $\rm M_{\oplus}$. Using an injection-recovery exercise, we find
that HD 190007 b and HD 216520 b are unlikely to have additional planets with
masses and orbital periods within a factor of two, in marked contrast to
$\sim$85\% of planets in this mass and period range found with Kepler.
