Bind C-h in tmux copy mode

I'm trying to bind C-h to move to the window on the left. Here is my tmux.conf set -g default-terminal "xterm-256color" bind -n S-down new-window bind -n C-l next bind -n C-h prev bind q killp unbind C-b set-option -g prefix C-space bind-key C-a send-prefix bind c new-window -a set-option -g history-limit 20000 set -g pane-border-style 'fg=colour1' All of these bindings work as expected in normal mode. In copy mode, they all work except C-h, which still functions as backspace and just moves the cursor left. I'm using Vi global bindings so I guess that's why. Is is possible to overwrite this Vi binding? I've tried adding unbind-key C-h first, makes no difference. The output of tmux list-keys -T copy-mode-vi | grep cursor-left is:

bind-key -T copy-mode-vi C-h send-keys -X cursor-left
bind-key -T copy-mode-vi h send-keys -X cursor-left
bind-key -T copy-mode-vi BSpace send-keys -X cursor-left
bind-key -T copy-mode-vi Left send-keys -X cursor-left