We study properties of the embedding operators of model sub-spaces K _Δ^p(defined by inner functions) in the Hardy space H^p(coinvariant subspaces of the shift operator). We find acriterion for the embedding of K_Δ^P in L^p(μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give apositive answer to aquestion of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in K_Δ^P. We investigate measures such that the embedding operator belongs to some Schatten-vonNeumann ideal.