Proofs of results announced earlier are given. Theorem 1, which was announced in 1976, states that a function on a domain with bounded boundary rotation can be approximated in terms of a function p₁^*(z), which modifies the classical distance p _1/n^α(z) for the points whose neighborhoods contain more than one arc of the level curve of the complement of the domain. Theorem 2, which was announced in 1977, provides a domain with bounded boundary rotation and a function in the analytic Hölder α-class on the domain which cannot be approximated with precision P_1/nα(z) by polynomials.