The ability To customize The incident x-ray fluence in CT via beam-shaping filters or mA modulation is known To improve image quality and/or reduce radiation dose. Previous work has shown That complete control of x-ray fluence (ray-by-ray fluence modulation) would further improve dose efficiency. While complete control of fluence is not currently possible, emerging concepts such as dynamic attenuators and inverse-geometry CT allow nearly complete control To be realized. Optimally using ray-by-ray fluence modulation requires solving a very high-dimensional optimization problem. Most optimization Techniques fail or only provide approximate solutions. We present efficient algorithms for minimizing mean or peak variance given a fixed dose limit. The reductions in variance can easily be Translated To reduction in dose, if The original variance met image quality requirements. For mean variance, a closed form solution is derived. The peak variance problem is recast as iterated, weighted mean variance minimization, and at each iteration it is possible To bound The distance To The optimal solution. We apply our algorithms in simulations of scans of The Thorax and abdomen. Peak variance reductions of 45% and 65% are demonstrated in The abdomen and Thorax, respectively, compared To a bowtie filter alone. Mean variance shows smaller gains (about 15%).