  The Honeymoon Oberwolfach Problem HOP$(2m_1,2m_2,\ldots,2m_t)$ asks the
following question. Given $n=m_1+m_2+\ldots +m_t$ newlywed couples at a
conference and $t$ round tables of sizes $2m_1,2m_2,\ldots,2m_t$, is it
possible to arrange the $2n$ participants at these tables for $2n-2$ meals so
that each participant sits next to their spouse at every meal, and sits next to
every other participant exactly once? A solution to
HOP$(2m_1,2m_2,\ldots,2m_t)$ is a decomposition of $K_{2n}+(2n-3)I$, the
complete graph $K_{2n}$ with $2n-3$ additional copies of a fixed 1-factor $I$,
into 2-factors, each consisting of disjoint $I$-alternating cycles of lengths
$2m_1,2m_2,\ldots,2m_t$.
  The Honeymoon Oberwolfach Problem was introduced in a 2019 paper by Lepine
and \v{S}ajna. The authors conjectured that HOP$(2m_1,2m_2,\ldots,$ $2m_t)$ has
a solution whenever the obvious necessary conditions are satisfied, and proved
the conjecture for several large cases, including the uniform cycle length case
$m_1=\ldots=m_t$, and the small cases with $n \le 9$. In the present paper, we
extend the latter result to all cases with $n \le 20$ using a computer search.
