I see no contradiction between Frank R. Palmer's definitions and mine. The limitation or difficulty in obtaining success in these two sentences:
I could almost reach the branch.
I could just reach the branch.
arises from the presence of the adverbs "almost" (limited success) and "just" (also "barely"), meaning success with difficulty.
By the way, you might find it of interest to read this discussion I had with David more than three years ago.