How to change max_allowed_packet size

I am having a problem with BLOB fields in my MySQL database - when uploading files larger than approx 1MB I get an error `Packets larger than max_allowed_packet are not allowed.` Here is what i've tried: In MySQL Query Browser I ran a `show variables like 'max_allowed_packet'` which gave me 1048576. Then I execute the query `set global max_allowed_packet=33554432` followed by `show variables like 'max_allowed_packet'` - it gives me 33554432 as expected. But when I restart the MySQL server it magically goes back to 1048576. What am I doing wrong here? Bonus question, is it possible to compress a BLOB field?