The behavior of the power efficiency Peff of an optical fiber with a bulk distribution of source in its cladding is analyzed. The expressions derived make use of the exact field solution of a cylindrical fiber, whereas previous work has made use of the weakly guiding approximation. Although more complicated and harder to interpret, the formulas presented allow the analysis of the power injection efficiency of fibers with arbitrary differences in indices of refraction. The results obtained are relevant to the design of more efficient optical fiber fluorosensors. The conclusions follow. Previous results using the weakly guiding approximation were confirmed. However, we have found that Peff does not always increase with the V number; it does, however, increase with the difference in the indices of refraction, ncore - nclad, and the wavelength λ. It also decreases with the fiber core radius a. Finally, a new independent variable, a/λ, was found.