In the double kernel density estimate, the smoothing parameter h is chosen so as to minimize the L\ distance between two kernel density estimates having identical smoothing factors but different kernels. This method is known to be consistent for any density and to be asymptotically optimal for a certain smooth class of densities. We propose a plug-in modification of the estimate and introduce various other data-based bandwidth estimates. Finally, a simulation study is presented in which the new bandwidth selectors are compared with a host of well-known methods.