We study the purely topological restrictions on allowed spin and statistics of topological solitons in nonlinear sigma models. Taking as space the connected d-manifold X, and considering nonlinear sigma models with the connected manifold M as target space, topological solitons are given by elements of π d (M ). Any topological soliton α ∈ π d (M ) determines a quotient Stat n (X, α) of the group of framed braids on X, such that choices of allowed statistics for solitons of type α are given by unitary representations of Stat n (X, α) when n solitons are present. In particular, when M = S 2 , as in the O(3) nonlinear sigma model with Hopf term, and α ∈ π 2 (S 2 ) is a generator, we compute that Stat n (R 2 , α) = Z, while Stat n (S 2 , α) = Z 2n . It follows that phase exp(iθ) for interchanging two solitons of type α on S 2 must satisfy the constraint θ = kπ/n, k ∈ Z, when n such solitons are present.