Trying plucking out the bass notes and alternately brushing or finger-picking the higher strings (how's that for precise musicological terminology?). Once you get used to it, you can "walk" through a bass melody while playing and singing, and it helps to maintain a steady rhythm throughout the song. I also find it easier to carry melodies when I'm not strumming four, five or six notes all at once. And yes, substitute an A minor for a C major (for example) if it sounds appropriate for a particular song.