  For a given unramified extension $K/K_1$ of finite extensions of
$\mathbb{Q}_p$, we effectively determine the number of finite Galois extensions
$L/K_1$ with maximal unramified subextension $K/K_1$ and a single wild
ramification jump at $2$. In fact, we determine explicit formulas in the cases
when $K_1/\mathbb{Q}_p$ is totally ramified and when it is unramified. This
builds upon the tamely ramified case, which is a classical consequence of
Serre's Mass Formula, exhibiting a more restrictive behavior than in the tamely
ramified case because the degrees of such extensions are bounded. As a
consequence of the calculation, it is also found that the count depends only on
the extension $k/k_1$ of residue fields.
