I looked around and I didn't see a binding for "repeat-complex-command".
When I run emacs -q it tells me the default bindings are:

<again>, <redo>, C-x M-:, C-x M-ESC.

It's been a long time since I've had an "again" key on my keyboard and
I've never had a "redo" key.  The other 2 bindings are just plain nuts.
(IMO).

So, pick a key, any key, but you really want a single key assigned to
this command.

So I use xmodmap to create an F19 key and assign it to the "extra"
"page up" key in the 6 key pad.  Then I bind it like this:

(define-key global-map [(f19)] 'repeat-complex-command);; Again Key
(define-key minibuffer-local-map [(f19)] 'previous-history-element);; Again Key
(define-key minibuffer-local-map [(shift f19)] 'next-history-element);; Again Key

So, the Page Up key brings up the last "complex" command.
Keep hitting the key and you see the history.
Press shift if you go to far.

I find myself using this a lot.

I find this second binding on the same key logical:

(define-key global-map [(S-f19)] 'call-last-kbd-macro);; Shifted Again Key

Same key, but start out holding down shift and you can re-execute that
keyboard macro with one key.

--
Dan Espen