The Head - No Need to Memorize Entire Song
Did you know that when most professionals do a cover song that they learn the head (the opening twelve bars... the most discernible part of the song) and then improvise the body? This takes a lot of the stress out of "memorizing" a song... learn the head and improvise everything else. If you're at the skill level where what you improvise comes close to sounding as good as what the original player of the song did, then this is the way to go.
For more information about heads and their construction, visit the lesson "Improvising Study 7 - Heads, Hooks, Bridges, Arrangement & Tribute Writing and Soloing Themes"