We present a more efficient version of the temperature accelerated dynamics (TAD) method. Without introducing any new approximation, we show how it is possible to make the TAD method faster when a system visits a state more than one time. We demonstrate the method for the diffusion of silver tetramers on Ag(100), obtaining an additional boost (relative to standard TAD) of similar to4 at T=400 K and similar to11 at T=200 K. Larger boosts can be obtained at lower temperatures and/or for different systems. This new formalism also offers a way to gain this additional boost in the dynamics on the first visit to a state, provided information is available about the lowest barrier for escape from the state.