  The Harary-Hill conjecture states that for every $n>0$ the complete graph on
$n$ vertices $K_n$, the minimum number of crossings over all its possible
drawings equals \begin{align*} H(n) :=
\frac{1}{4}\Big\lfloor\frac{n}{2}\Big\rfloor\Big\lfloor\frac{n-1}{2}\Big\rfloor\Big\lfloor\frac{n-2}{2}\Big\rfloor\Big\lfloor\frac{n-3}{2}\Big\rfloor\text{.}
\end{align*} So far, the lower bound of the conjecture could only be verified
for arbitrary drawings of $K_n$ with $n\leq 12$. In recent years, progress has
been made in verifying the conjecture for certain classes of drawings, for
example $2$-page-book, $x$-monotone, $x$-bounded, shellable and bishellable
drawings. Up to now, the class of bishellable drawings was the broadest class
for which the Harary-Hill conjecture has been verified, as it contains all
beforehand mentioned classes. In this work, we introduce the class of
seq-shellable drawings and verify the Harary-Hill conjecture for this new
class. We show that bishellability implies seq-shellability and exhibit a
non-bishellable but seq-shellable drawing of $K_{11}$, therefore the class of
seq-shellable drawings strictly contains the class of bishellable drawings.
