  We show that efficient geodesics have the strong property of "super
efficiency". For any two vertices, $v , w \in \mathcal{C}(S_g)$, in the complex
of curves of a closed oriented surface of genus $g \geq 2 $, and any efficient
geodesic, $v = v_1 , \cdots , v_{{\text d}}=w$, it was previously established
by Birman, Margalit and the second author (see arXiv:1408.4133) that there is
an explicitly computable list of at most ${\text d}^{(6g-6)}$ candidates for
the $v_1$ vertex. In this note we establish a bound for this computable list
that is independent of ${\text d}$-distance and only dependent on genus -- the
super efficiency property. The proof relies on a new intersection growth
inequality between intersection number of curves and their distance in the
complex of curves, together with a thorough analysis of the dot graph
associated with the intersection sequence.
