A weight-dependent capability is inserted into the direct statistical approach (DSA) to optimize splitting and Russian roulette (RR) parameters in Monte Carlo particle transport calculations. In the new model, splitting or RR is carried out on a progenitor arriving at a surface in such a way that the weight of the progeny is fixed (for the particular surface). Thus, the model is named the DSA weight tine model. In the presence of weight-dependent games, all components of the second moment, and the time, are not separable. In the absence of weight-dependent games, the component of the second moment describing the weight-dependent splitting or RR is still not separable. Two approximations are examined to render this component separable under these circumstances. One of these approximations, named the noninteger approximation, looks promising. The new DSA model with the noninteger approximation is tested on four sample problems. Comparisons with the previous weight-independent DSA model and with the MCNP (version 4a) weight window generator are made.