A single pass UV or X-ray FEL will require a low emittance electron beam with high peak current and relatively high beam energy, a few hundred MeV to many GeV. To achieve the necessary peak current and beam energy, the beams must be bunch compressed and they must be accelerated in long transport lines where dispersive and wakefield emittance dilutions are important. In this paper, we will describe the sources and significance of the dilutions during acceleration, bunch compression, and transport through the undulator. In addition, we will discuss sources of jitter, especially effects arising from the bunch compressions, and the possible cancellation techniques.