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Abstract. Let be the automorphic representation of GSp4(A) generated by a full level cuspidal Siegel eigenform that is not a Saito-Kurokawa lift, and be an arbitrary cuspidal, automorphic representation of GL2(A). Using Furusawa's integral represen-tation for GSp4 GL2 combined with a pullback formula involving the unitary group GU(3; 3), we prove that the L-functions L(s; ) are \nice". The converse theorem of Cogdell and Piatetski-Shapiro then implies that such representations have a functo-rial lifting to a cuspidal representation of GL4(A). Combined with the exterior-square lifting of Kim, this also leads to a functorial lifting of to a cuspidal representation of GL5(A). As an application, we obtain analytic properties of various L-functions related to full level Siegel cusp forms. We also obtain special value results for GSp4GL1 an