Once-punctured Klein bottles in knot complements

We find the family of all knots in S3 which are spanned by two essential once-punctured Klein bottles with boundary slopes at distance 4, thus settling a conjecture by K. Ichihara, M. Ohtouge, and M. Teragaito. We also address the more general question of when a knot exterior in an arbitrary 3-manifold contains two essential once-punctured Klein bottles with distinct boundary slopes.