  This paper characterises the dual of the model space $K_I^1$, where $I$ is an
inner function, intersected with the shifted Hardy space, $z H^1$. With this
duality result, it is then shown that every bounded truncated Toeplitz operator
on the model space $K_I^2$ has a bounded symbol if and only if every compact
truncated Toeplitz operator on $K_I^2$ has a symbol which is of the form $I$
multiplied by a continuous function.
