We present a search for WW and WZ production in final states that contain a charged lepton (electron or muon) and at least two jets, produced in root s = 1.96 TeV p (p) over bar collisions at the Fermilab Tevatron, using data corresponding to 1.2 fb(-1) of integrated luminosity collected with the CDF II detector. Diboson production in this decay channel has yet to be observed at hadron colliders due to the large single W plus jets background. An artificial neural network has been developed to increase signal sensitivity, as compared with an event selection based on conventional cuts. We set a 95% confidence level upper limit of sigma(WW) x BR(W -> l nu(l), W -> jets) + sigma(WZ) x BR(W -> l nu(l), Z -> jets) < 2.88 pb, which is consistent w...