Thanks for the excellent comments and apologies for the time it's taken for me to reply. Indeed, I understand about most combined verbs but there are some pairs, like 取り囲む/囲む, that seem so similar in meaning that one must wonder about the difference. Due to the information presented in these posts, however, I believe I have a much better idea of what's going on (and how to look up such things in the future). Many thanks to all!