Collisions between vapor monomers and small clusters may create short-lived states that will decay before undergoing equilibriating collisions with other (vapor or gas) molecules. As the vapor pressure (and hence the number of monomer-cluster collisions) increases, the number of such decays will increase, in contrast to the usual assumption that cluster decay rates are independent of the external vapor pressure. Such short-lived clusters should therefore be excluded from consideration in nucleation theory. The effect of excluding clusters with lifetimes less than a specified value tau is investigated by evaluating the partition function for clusters of 2, 3, and 4 molecules interacting via a Lennard-Jones potential. Calculations are performed by Monte Carlo integration, with a molecular dynamics simulation performed at each Monte Carlo point to determine whether the monomers remain within a specified distance of their center of mass a time tau later. Results are compared with those from other cluster definitions, including classical theory and constant volume clusters. Values are approximately independent of tau provided it is not too small, and exhibit a stronger decrease with increasing temperature than those from other cluster definitions. Making classical nucleation theory consistent with the population of long-lived small clusters (instead of with the monomer population) would therefore reduce the temperature dependence of theory.