  We consider the CFT of a free boson compactified on a circle, such that the
compactification radius $R$ is an irrational multiple of $R_{selfdual}$. Apart
from the standard Dirichlet and Neumann boundary states, Friedan suggested [1]
that an additional 1-parameter family of boundary states exists. These states
break U(1) symmetry of the theory, but still preserve conformal invariance. In
this paper we give an explicit construction of these states, show that they are
uniquely determined by the Cardy-Lewellen sewing constraints, and we study the
spectrum in the `open string channel', which is given here by a continous
integral with a nonnegative measure on the space of conformal weights.
