LetRbe an algebra over a fieldk. We say that an idealIofRisco-generatedby a setFofk-linear functionalsR→kifIis the largest ideal ofRthat is contained in the kernels of all the functionals inF;. We will state sufficient conditions for an ideal of a freek-algebra to be co-generated by finitely many functionals. We then get as a corollary that every ideal of the polynomial algebra over a field in finitely many variables is finitely co-generated. This is a known result, but the way we construct the co-generators in the general case, leads to that we get a tight bound on how many co-generators are needed for such ideals.