Computes a smooth canonical curve of genus g over a field of characteristc p. The constructions are based on the unirationality proofs of Mg for g<=10 and the methods in the RandomCurves-package. A unirational parametrization of Mg is only a rational map and bad choices of parameters (which are quite likely over small fields) might end up in the indeterminacy locus or some other undesired subloci. In this constructions we catch the steps which do not work out for very small characteristic. The Function works for 11<=g<=13.