Several approaches exist for maintaining consistency in Distributed Interactive Applications. Among these are techniques such as dead reckoning which use prediction algorithms to approximate actual user behaviour and thus reduce the number of update packets required to maintain spatial consistency. The Hybrid Strategy Model operates in a similar way, exploiting long-term patterns in user behaviour whenever possible. Otherwise it simply adopts a short-term model. A major problem with these techniques is the reconstruction of the local behaviour at a remote node. Using the modelled dynamics directly can result in unnatural and sudden jumps in position where updates occur. Convergence algorithms are thus required to smoothly reconstruct remote behaviour from discontinuous samples of the actual local behaviour. This paper makes two important contributions. Primarily, it proposes a novel convergence approach for the Hybrid Strategy Model. Secondly, and more fundamentally, it exposes a lack of suitable and quantifiable measures of different convergence techniques. In this paper the standard smoothing algorithm employed by DIS is used as a benchmark for comparison purposes.