Emacs: Combine iseach-forward and recenter-top-bottom

Thank you very much in advance for helping.

In Emacs, I like to use iseach-forward (C-s) but I'd like it ever more if the highlighted fount words would be centered in the middle of the screen instead of at the very bottom.

I find myself doing this continuously:

C-s foo C-s C-s C-s... oh! that's the 'foo' I was looking for! C-l

Is there a way to center the search results in the middle of the screen?

Cheers