Leonard Cohen

I like the fella, but:

"Like a bird on the wire,
Like a drunk in a midnight choir,
I have tried in my way to be free."

I'm afraid I just don't understand this.
How is a bird on a wire - or indeed a drunk in a midnight choir (I'm guessing this must be at midnight mass on Christmas Eve) - trying to be free? Any more than a fish in a bowl, an okapi in a small copse or two firemen in a van on their way to a football match on their day off?

OK, I accept that the thing wouldn't scan as well if you used any of those lyrical options...