We report the detection of two short-period planets discovered at Keck Observatory. HD 149143 is a metal-rich G0 IV star with a planet of Msini=1.33MJ and an orbital radius of 0.053 AU. The best-fit Keplerian model has an orbital period, P=4.072 days, semivelocity amplitude, K=149.6 m s-1, and eccentricity, e=0.016+/-0.01. The host star is chromospherically inactive and metal-rich, with [Fe/H]=0.26. Based on the Teff and stellar luminosity, we derive a stellar radius of 1.49 Rsolar. Photometric observations of HD 149143 were carried out using the automated photometric telescopes at Fairborn Observatory. HD 149143 is photometrically constant over the radial velocity period to 0.0003+/-0.0002 mag, supporting the existence of the planetary companion. No transits were detected down to a photometric limit of approximately 0.02%, eliminating transiting planets with a variety of compositions and constraining the orbital inclination to less than 83°. A short-period planet was also detected around HD 109749, a G3 IV star. HD 109749 is chromospherically inactive, with [Fe/H]=0.25 and a stellar radius of 1.24. The radial velocities for HD 109749 are modeled by a Keplerian with P=5.24 days and K=28.7 m s-1. The inferred planet mass is Msini=0.28MJ and the semimajor axis of this orbit is 0.0635 AU. Photometry of HD 109749 was obtained with the SMARTS consortium telescope, the PROMPT telescope, and by transitsearch.org observers in Adelaide and Pretoria. These observations did not detect a decrement in the brightness of the host star at the predicted ephemeris time, and they constrain the orbital inclination to less than 85° for gas giant planets with radii down to 0.7RJ.Based on observations obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration (NASA). The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Keck time has been granted by the National Optical Astronomy Observatory (NOAO) and NASA.