How to quickly send commands to nested tmux sessions?

It is one less keypress to send a command to your nested session if you choose a different key. I use Ctrlt for my standard prefix, and Ctrla for nested sessions.

# set prefix key to ctrl+t
unbind C-b
set -g prefix C-t

# send the prefix to client inside window
bind-key -n C-a send-prefix

Note that I use the -n switch. From the bind-key entry in man tmux:

if -n is specified, it is not necessary to use the prefix key, command is bound to key alone.

So, as an example, Ctrlt, c opens a new window in tmux; Ctrla, c does the same in the nested session.