1. Let X be the unit circle Iz I = 1, and A the "disc algebra" of functions on X having continuous extensions to I z ? < 1 analytic for I z I < 1. Then it is known [12] that there is no bounded projection of C(X) onto A; alternatively, A is uncomplemented in C(X). To what extent is this a general occurrence? Specifically, if A is a closed nonselfadjoint(2) subalgebra of C(X), X compact, is A uncomplemented in C(X)? Only some partial results will emerge here. From recent results of Bishop [1], extended to the nonmetric case by Bishop and deLeeuw in [2], we obtain the curious fact that if X is the Silov boundary of A, and T is any bounded operator on C(X) acting as the identity on A, then T I || = 11 T |1, where I is the identity operator; alternatively, any operator S (= I T) annihilating A has || I + S || = 1 + || S ||. As a consequence of this fact one can apply the technique of [12] to show that if X is a compact group and our nonselfadjoint subalgebra A of C(X) is translation invariant, A is uncomplemented; in fact any closed subspace lying between two invariant algebras A1 c A2, with the set of conjugates A1 t A2, is uncomplemented (?3). And this applies equally well to invariant subalgebras A1, A2 of(3) CO(X), where X is a locally compact abelian group (?4); but both proofs are technically complicated, and shed no light on the situation in general. In what follows we shall consider a slightly more general setting in which A is a subalgebra of CO(X), X locally compact; since we shall be concerned with estimating the norms of projections, the usual adj unction of an identity does not lead easily to a reduction to the compact case. The author is indebted to K. deLeeuw for several helpful comments and, in particular, Theorem 4.1 is due to deLeeuw.