  We consider a relativistic no-pair model of a hydrogenic atom in a classical,
exterior magnetic field. First, we prove that the corresponding Hamiltonian is
semi-bounded below, for all coupling constants less than or equal to the
critical one known for the Brown-Ravenhall model, i.e., for vanishing magnetic
fields. We give conditions ensuring that its essential spectrum equals
[1,\infty) and that there exist infinitely many eigenvalues below 1. (The rest
energy of the electron is 1 in our units.) Assuming that the magnetic vector
potential is smooth and that all its partial derivatives increase
subexponentially, we finally show that an eigenfunction corresponding to an
eigenvalue \lambda<1 is smooth away from the nucleus and that its partial
derivatives of any order decay pointwise exponentially with any rate
a<(1-\lambda^2)^{1/2}, for \lambda\in[0,1), and a<1, for \lambda<0.
