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 s√=1.96  TeV pp 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 σWW×BR(W→ℓνℓ,W→jets)+σWZ×BR(W→ℓνℓ,Z→jets)<2.88  pb, which is consistent with the standard model next-to-leading-order cross section calculation for this decay channel of 2.09±0.12  pb.