Tee all output to log file?

["Benjamin R. Haskell" <zsh@xxxxxxxxxx>]

For scripting purposes I occasionally want a way to both record and 
display all the output of a script.  On several occasions now, I've 
looked through the output redirection section of the manual, but I never 
come up with quite what I'm looking for.

Essentially, when I want this, I usually want something like:

#!/bin/zsh
(( $+logfile )) && exec |& tee $logfile

Boiled down even further, it's really just this I'm looking for:
exec |& tee logfile

Is there something straightforward that I'm overlooking?  Is there a 
commonly used utility for this?  (`script` comes to mind, but I recall 
klunkiness when trying it in the past.)

--
Best,
Ben