Relative oscillator strengths are measured for nine very weak 1-eV Fe I lines, using the Oxford spectroscopic furnace. These oscillator strengths are placed on an absolute scale using previous Oxford measurements of stronger 1-eV Fe I lines. The lines are important for the interpretation of cool star spectra because they are the weakest Fe I lines in such spectra whose oscillator strengths are known with good accuracy. Their accuracy is assessed through an interpretation of the corresponding lines in the center of disk solar spectrum. It is suggested that the accuracy is 0.015 dex (3.5 percent).