The blue metal-poor (BMP) star CS 22966-043 is an SX Phoenicis star and the primary of a spectroscopic binary with a provisional orbital period of ~430 days. Radial velocity and UBV photometric observations of this star made in 1998 require downward revision of the orbital period to 319 days. The BMP star CS 29499-057 also appears to be an SX Phoenicis star with small amplitude (ΔV ~ 0.04 mag) and short period (P = 0.0417 days), on the basis of photometric and radial velocity observations obtained in 1998. There is some indication that it too may be the primary of a spectroscopic binary. Three other BMP stars have radial velocity standard deviations greater than those of 17 BMP radial velocity standards. We suggest that they may be small-amplitude SX Phoenicis stars. Finally, the BMP star CS 29497-017 is shown to be a short-period velocity variable (P = 0.302 days) on the basis of observations accumulated over an interval of 2200 days, but we were unable to detect a light variation in 1998 July. Therefore, the nature of the velocity variation of this object remains uncertain.