We present a new approach and improvements to the recent results of Gabai, Meyerhoff and Milley concerning tubes and short geodesics in hyperbolic
3
3
-manifolds. We establish the following two facts: if a hyperbolic
3
3
-manifold admits an embedded tubular neighbourhood of radius
r
0
>
1.32
r_0>1.32
about any closed geodesic, then its volume exceeds that of the Weeks manifold. If the shortest geodesic of
M
M
has length less than
ℓ
0
>
0.1
\ell _0>0.1
, then its volume also exceeds that of the Weeks manifold.