Methods and apparatus for determining encoding parameters of an encoder or a transcoder which yield an encoded signal of optimal measurable properties are disclosed. For a video signal, the encoding parameters may include quantization granularity, a measure of display resolution, and a frame rate. The measurable properties of an encoded signal may include a fidelity index, a relative size, and a relative flow rate. Reference data records quantifying properties of sample signals encoded according to experimental sets of encoding parameters are used to define parameters of conjectured analytical functions characterizing the encoding or transcoding functions. The analytical functions are then used to generate granular tables of estimated measures of encoded-signal properties. A fast search mechanism relies on the granular tables, together with sorted arrangements of the granular tables, to determine, in real-time, preferred encoding parameters for multimedia data streams received at an encoder or a transcoder.