Band oscillator strengths (f-values) for four bands of the Fourth Positive system (A1PI-X1SIGMA+) of CO have been determined from high-resolution (lambda/DELTAlambda almost-equal-to 150,000) absorption spectra. The bands, (14, 0) through (11, 0), are at wavelengths between 121 and 127 nm. Our f-values for the (I 1, 0) and (I 2, 0) bands support those of Chan, Cooper, & Brion (1993), which have been shown to be consistent with observations of CO in the clouds in the line of sight, to zeta Oph. Our f-values for the (13, 0) and (14, 0) bands are the first directly measured values for these bands.