  We consider the online two-dimensional vector packing problem, showing a
lower bound of $11/5$ on the competitive ratio of any {\sc AnyFit} strategy for
the problem. We provide strategies with competitive ratio
$\max\!\left\{2,6\big/\big(1+3\tan(\pi/4-\gamma/2)\big)+\epsilon\right\}$ and
logarithmic advice, for any instance where all the input vectors are restricted
to have angles in the range $[\pi/4-\gamma/2,\pi/4+\gamma/2]$, for
$0\leq\gamma<\pi/3$ and
$\max\left\{5/2,4\big/\big(1+2\tan(\pi/4-\gamma/2)\big)+\epsilon\right\}$ and
logarithmic advice, for any instance where all the input vectors are restricted
to have angles in the range $[\pi/4-\gamma/2,\pi/4+\gamma/2]$, for
$0\leq\gamma\leq\pi/3$. In addition, we give a $5/2$-competitive strategy also
using logarithmic advice for the unrestricted vectors case. These results
should be contrasted to the currently best competitive strategy, FirstFit,
having competitive ratio~$27/10$.
