My 2 dollars.... (

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First of all - the better the song, the EASIER to remember it.
A song that's well written, with meaningful changes and lyrics makes much more sense, and is easier to stick in MY mind.
My method is simple - I prioritize....
1) vocals - READ the words, out loud. Don't sing, READ the words, in a spoken voice. This forces the brain to "listen" to the lips. If the words make sense, they will stay with you longer.
2) chords/bass - equally important. In my case, I hear the bass lines easier, because I spent many years as a bass player. Laying down the "foundation" makes it MUCH easier to add the chords and embellish lines afterwards. If the vocals and bass are right ..... you're ALMOST there. Bass, vocals and drums are a complete tune. The rest is "fluff"....and we all LOVE our fluff !
3) WRITE the chart out. This is very effective. Something "clicks" in my brain when I write. I don't read on stage ..... I just write it out as I practice the tune. It really "cements" the song in my head. Makes a mental "snapshot" of the page, I guess.
4) Imagine the song as a short play. If you "get into character" you'll associate with the song meaning and it'll speak to you. If it MEANS something .... you'll WANT to remember it! Our brains remember TONS of numbers, names, faces ........ that are trivial to our lives. Imagine how easy it will be to remember stuff that is IMPORTANT or personal to you! Act out each song as if it were a play .... and you'll get so much more from it.
I've said many times, the only time that you truly "own" a performance is when you can do it from memory. You need ALL your concentration to "sell" a number, and if you are expending energy reading a chart ..... you are being DISTRACTED. It's a fact of life. Road maps, cheat sheets .... call them what you will, but leave them in the car, or on the floor. I'd rather flub a word or two than have my eyes glued (yeah, yeah .. even for a second!) to a page. People are starved for real energy in live performances these days. Superstars "lip Sync", and sequencers "play" the band's parts, and little by little we are taking the musician OUT of the music.
I strongly urge you all to memorize as much as possible, and see what I mean.
It's one thing to read a special wedding song, or an obscure request, but C'mon folks ...... I have a friend who still reads the words to "Misty" after 30 years !!!! AAGH !