This paper reports preliminary measurements on the properties of cryogenic sapphire resonators with various concentrations of paramagnetic impurities. These resonators have been mounted in both copper and niobium shields. We have found that we can achieve extrema in the frequency-temperature function in the temperature range 5-18 K due to the compensating effects of the dielectric constant temperature dependence and the Curie law dependence of the susceptibility of the paramagnetic impurities. In sapphire samples with dominant impurities Cr3+ and Fe3+, we find strong influences on the mode frequency when we are near the electron spin resonances (ESR) at 11.45 GHz and 12.04 GHz, respectively, and no extrema occurs when we are above the ESR frequency. In samples where dominant paramagnetic impurity has a high ESR we get an essentially frequency independent frequency-temperature compensation. In these samples we have observed unloaded resonator Q factors as high as 4 x 10(9). The increased Q factors coupled with reduced shield interactions should result in an improvement in frequency stability for an oscillator based around this resonator as compared to the best results achieved to date at this laboratory (an Allan Variance of 9 x 10(-15)). We report the preliminary measurement of the tilt sensitivity of our oscillator to be a fractional frequency shift of 6.5 x 10(-12) per degree.