We investigate compactness and asymptotic behaviour of the entropy numbers of embeddings B s1,s1 p1,q1 (Rn , U) → B s2,s2 p2,q2 (Rn , U) . Here Bs,s p,q (Rn, U) denotes a 2-microlocal Besov space with a weight given by the distance to a fixed set U ⊂ Rn.