The notion of a weakly scattered theory T is defined. T need not be scattered. For each $\cal A$ a model of T, let sr($\cal A$) be the Scott rank of $\cal A$. Assume sr($\cal A$) ≤ ω\sp A \sb 1 for all $\cal A$ a model of T. Let σ\sp T \sb 2 be the least Σ₂ admissible ordinal relative to T. If T admits effective k-splitting as defined in this paper, then $∃θ < σ\sp T \sb 2 such that sr($\cal A$) < θ for all $\cal A$ a model of T.