Leave things implied. Allow a character's "character" show me who they are. If Joe is traumatized by his experiences in a war, you don't need to say "Joe is traumatized by his experiences in the war," make him stutter, or appear anxious a lot, or claustrophobic while riding a subway car in through a dark tunnel and have him freak out. Show who your characters are, so I can make up my own mind about them. If you just tell me "Sam is sad," what do I actually get out of that? What is sad? What do I see in that? I see a word--SAD. Nothing else. I don't give a damn about him. Show that he's sad, or troubled, or hard-nosed, and allow me to decide on my own, and maybe I'll actually start caring about what happens to him/her.
Long answer short...to avoid an info dump, simply don't write one. Show, don't tell, who and what your characters are.
EDIT: I just read the part about you saying that information needs to be revealed quickly after a character's introduction...WRONG. Not right. We don't NEED to know anything about a character immediately. Allow their actions, attitude, speech patterns, mannerisms, etc. to reveal these things to us. Imply, imply, imply. Readers aren't as stupid as we like to think sometimes.