Dual energy CT scanning (tomochemistry) has been proposed as a method for determining various parameters relating to the elemental composition of the tissues. In this paper, our aim is to study the relative noise inherent in two proposed techniques for dual energy scanning; a "two crystal" technique and a "two kV" technique. In the two crystal technique, a split crystal detector is used to simultaneously obtain the high and low energy data during one scan at high kV. The two kV technique requires two scans taken with widely different kV settings. We first review three commonly used approaches for utilizing the scan data to compute the relevant parameters. A theoretical formalism is constructed which aids in understanding these methods. Then this formalism is used to study the influence of CT image noise on measurement precision in the case where the unknown parameters are densities. It is shown that, (1) the unavoidable overlap in the spectral data obtained by the two crystal technique results in a much lower signal-to-noise ratio than can be obtained by using the two kV technique, (2) the necessity for hard filtration of the high energy beam in the two kV technique has not heretofore been appreciated, and (3) the dose for a given x-ray tube heat load is also lower with the two kV technique.