Olive Tree Pruning?
Hi - I purchased an arbequina olive tree recently and it's about 3.5 feet tall, but only the thickness of a pencil. It seems as though it can barely hold up its long limbs (slightly smaller than the thickness of a pencil). In fact, two of the limbs appeared to have died right after I brought it home, so I cut those back to about 3" (right before the death). It seems to be doing ok, but it's obviously very spindly still. I want to know if I should prune it to hopefully encourage it to grow a thicker trunk. It has two very long branches left, and about four short ones.
Some other notes: It put on buds soon after I brought it home and many of them have opened now, releasing a bunch of yellow pollen. It has been kept indoors, under a 150 watt metal halide lamp, in a large container (30G?).
Thanks for any help, and feel free to ask me anything about it if it would help come up with a solution.