In addition to Tig's post, you can also increase the lightmap resolution on the surfaces where the shadow is casting or on the level as a whole, this should increase the sharpness/definition of the shadow (at the expense of higher compile times).
To set a higher lightmap resolution for the whole level, create a '_lightmapscale' key on the worldspawn and set it to a value lower than 1. 0.5 will double the lightmap, 0.25 will quadruple it, and 0.125 is 8x I think. You can go even lower but it's diminishing returns and the compile times start to get crazy.
To set a higher lightmap scale on a subset of brushes and/or patches, put them in a func_group and set the _lightmapscale key on that func_group entity. Note that adding them to a func_group may make them non-solid so you may have to do some extra work to repair leaks.
If none of the above works you might also need to check that there are not multiple light sources modifying the tree's shadow - Multiple light sources will tend to make the shadow less defined, as they do in real life.
Edited 2 minutes after the original posting.