I agree Boyd - those Specialized Armadillos are a very tight fit. It took me 20 minutes to change my tyres over a few weeks ago - a job that would normally take under 10!
I commute on my bike most days and have done for about 10 years. As such I have had the majority of bike related incidents including punctures, broken chains, wheels coming adrift from frame (broken hub!) etc etc. I carry 1 inner tube, some leeches, some mini tyre levers, some cable ties (to fix a knackered cassette) and a multitool (Topeak) which includes a chain tool - and a pair of latex gloves! This fits easily into my small saddle bag and has saved my life on many occasions. The last thing that saved me coming home from work in London, one evening was my blockbusters video card - used it to line a torn tyre where the tear was too big!
I do carry a mini pump - Can not remember the make - I avoid the double action ones (now!) as they are not as strong in the stem and I quickly broke the one I had!
Regards
BB