H4 bulbs have 3 tabs precisely located to position the bulb's filaments at the proper focal point in the headlight reflector. See the graphic below for a diagram of how this can effect your headlight aim for both high and low-beam.
In general, tilting the bulb upward in the reflector will cause the high-beam to be low while the low-beam is even lower and at a larger angle from the high-beam. This is because the low-beam filament is further forward than the high beam. Since the bulb is tilted upward, the forward filament moves further than the rear one. Adjusting the reflector upward will only give you a low-beam that's correct and a high-beam that points at the trees.
You can fix this problem by slightly bending the two lower tabs forward to lower the filaments in the reflector. At some point you'll get the proper degree of angle between the high and low beam. Honda had it right originally but sloppy work with the Dremel or using other methods which eliminate the two lower tabs (such as the nail method) can lead to improper bulb position in the reflector.