We show that if a hyperbolic knot manifold
M
M
contains an essential twice-punctured torus
F
F
with boundary slope
β
\beta
and admits a filling with slope
α
\alpha
producing a Seifert fibred space, then the distance between the slopes
α
\alpha
and
β
\beta
is less than or equal to
5
5
unless
M
M
is the exterior of the figure eight knot. The result is sharp; the bound of
5
5
can be realized on infinitely many hyperbolic knot manifolds. We also determine distance bounds in the case that the fundamental group of the
α
\alpha
-filling contains no non-abelian free group. The proofs are divided into the four cases
F
F
is a semi-fibre,
F
F
is a fibre,
F
F
is non-separating but not a fibre, and
F
F
is separating but not a semi-fibre, and we obtain refined bounds in each case.