A vertex of a simple graph is called large if its degree is at least 3. It was shown recently that in the class of starlike trees, which have one large vertex, there are no pairs of cospectral trees. However, already in the classes of trees with two or three large vertices there exist pairs of cospectral trees. Thus, one needs to employ additional graph invariant in order to characterize such trees. Here we show that trees with two or three large vertices are characterized by their eigenvalues and angles.