All commercial 2-MHz and 400-kHz propagation resistivity logging-while-drilling (LWD) tools use an assumed value or relationship for dielectric permittivity to derive independent resistivities from phase shift and attenuation measurements. This methodology has been used for over ten years. For resistivities below 100 Ω-m, the phase shift resistivity is not strongly affected by the assumed value of dielectric constant. In contrast, the attenuation resistivity is sensitive to the assumed dielectric constant above 10 Ω-m, and extremely sensitive above 50 Ω-m. A new empirical relationship between relative dielectric constant and resistivity is proposed to improve the phase shift and attenuation resistivities above 100 Ω-m. However, in high resistivity formations, and in unusual lithologies with exceptionally large dielectric permittivities, it is better to invert the measured phase shifts and attenuations together to obtain an apparent resistivity that is independent of the dielectric constant. This "dielectric-independent" resistivity will be free of possible errors caused by assuming a wrong value for dielectric permittivity. Even though phase shift and attenuation resistivities exhibit different vertical and radial response characteristics, simulations show that bed boundaries and moderate invasion do not adversely affect the computation of the dielectric-independent resistivity. In oil based mud, it is possible to read resistivities above 1000 Ω-m. This provides the ability to differentiate among high resistivity formations, but not necessarily the ability to measure a quantitative value. Three field examples illustrate the strengths and limitations of the dielectric-independent resistivity.