Let M M and N N be smooth manifolds, where M ⊂ N M\subset N and dim ⁡ ( N ) − dim ⁡ ( M ) ≥ 3 \dim (N)-\dim (M)\ge 3 . A disjunction lemma for embeddings proved recently by Goodwillie leads to a calculation up to extension problems of the base point component of the space of smooth embeddings of M M in N N . This is mostly in terms of i m m ( M , N ) \mathbf {imm}(M,N) , the space of smooth immersions, which is well understood, and embedding spaces e m b ( S , N ) \mathbf {emb}(S,N) for finite subsets S S of M M with few elements. The meaning of few depends on the precision desired.