FYI, I am using Tmux through the Mac OS X Terminal app.
After a lot of research and spending time. I have found the best way for me on zsh and terminal.app
I am using prefix-c to clear the screen and prefix-C to clear the history and the scroll buffer and leaving no lines above because I find it annoying.
# clear screen
bind c send-keys 'C-l'
# clear screen and history
bind C send-keys -R \; send-keys C-l \; clear-history \; send-keys
# check if the pane is running vim
is_vim="ps -o state= -o comm= -t '#{pane_tty}' \ | grep -iqE '^[^TXZ ]+ +(\\S+\\/)?g?(view|n?vim?x?)(diff)?$'"
# clear screen
bind c if-shell "$is_vim" "send-keys c" "send-keys 'C-l'"
# clear screen and history
bind C send-keys -R \; send-keys C-l \; clear-history \; send-keys