We make a careful analysis of $W^pmgamma$ production at the LHC, identifying the $W^pm$ through leptonic decays, with a view to exploring the sensitivity of the machine to anomalous $CP$-conserving $WWgamma$ interactions. All the available kinematic variables are used, but we find that the most useful one is the opening angle in the transverse plane between the decay products of the $W^pm$. It is shown that even a simple-minded analysis using this variable can lead to a much greater sensitivity at the LHC than the current constraints on the relevant parameters.
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