This is possible in tree-style tabs.
Its very useful especially when searching google for something related to the content of the current page. So when you close the new google search tab, you immediately return back to the previous related tab.
However, it's also true that sometimes, you want to start a completely new search. Thus, in firefox, I have 2 keyboard shortcuts. One for opening a child tab. Another for opening a tab at the start/end of the tab bar.
This allows very efficient management of the tab tree without much "moving around".
Customer support service by UserEcho