It is proved that for each inner function
θ
\theta
there exists an interpolating sequence
{
z
n
}
\left \{ {{z_n}} \right \}
in the disk such that
sup
n
|
θ
(
z
n
)
|
>
1
{\sup _n}|\theta ({z_n})| > 1
, but every function
g
g
in
H
∞
{H^\infty }
with
g
(
z
n
)
=
θ
(
z
n
)
(
n
=
1
,
2
,
…
)
g({z_n}) = \theta ({z_n})(n = 1,2, \ldots )
satisfies
|
|
g
|
|
∞
≥
1
||g|{|_\infty } \geq 1
. Some results are obtained concerning interpolation in the star-invariant subspace
H
2
⊖
θ
H
2
{H^2} \ominus \theta {H^2}
. This paper also contains a "geometric" result connected with kernels of Toeplitz operators.