We present new radial velocity (RV) measurements of the ultra-cool dwarf VB 10, which was recently announced to host a giant planet detected with astrometry. The new observations were obtained using optical spectrographs (MIKE/Magellan and ESPaDOnS/CFHT) and cover 65% of the reported period of 270 days. The nominal precision of the new Doppler measurements is about 150 m/s while their standard deviation is 250 m/s. However, there are indications that such a larger variation is due to uncontrolled systematic errors. We apply least-squares periodograms to identify the most significant signals and evaluate their false alarm probabilities (FAPs). We show that this method is the proper generalization to astrometric data because (1) it mitigates the coupling of the orbital parameters with the parallax and proper motion, and (2) it permits a direct generalization to include nonlinear Keplerian parameters in a combined fit to astrometry and RV data. Our analysis of the astrometry alone uncovers the reported 270 day period and an even stronger signal at ∼50 days. We estimate the uncertainties in the parameters using a Markov chain Monte Carlo approach. Although the new data alone cannot rule out the presence of a candidate, when combined with published RV measurements, the FAPs of the best solutions grow to unacceptable levels strongly suggesting that the observed astrometric wobble is not due to an unseen companion. The new measurements put an upper limit of m sin i ∼ 2.5 mjup for a companion with a period shorter than one year and moderate eccentricities.