$A\_\infty$ operad can be described both in terms of Stasheff polytopes and configuration spaces.$A\_n$ operad can be described as subspace of Stasheff operad described using Stasheff polytope. Is there a model for $A\_n$-operad as a configuration spaces? 



A_n operad as configuration spaces
At the risk of saying something stupid I'm promoting my comment to an answer. In terms of the Stasheff polytopes the $A\_n$ operad sits inside the $A\_\infty$ operad as the union of all faces of dimension $\leq n-2$. Another way of saying this is that the Stasheff polytopes are stratified spaces with strata indexed by rooted trees. The $A\_n$ operad is defined as the union of all strata where each vertex of the tree has valence at most $n$.


Now another model of $A\_\infty$ operad is given by the sequence of Fulton-MacPherson compactifications of the configuration spaces of points on the interval. The Fulton-MacPherson compactification of any space is also naturally a stratified space, with strata indexed by rooted trees, and the same prescription should work to get a configuration space model of $A\_n$ operad.


