Here is a clever little tune by Dexter Gordon and Bud Powell. It is a straight-ahead AABA 32-bar form. The A sections mostly alternate between Fmaj7 concert and Gb7. The bridge is a little more involved, but manageable.
The challenge of this tune is the melody line, which you can find in many fake books. The lines are interesting, sometimes obtuse, and you can hear Ellington's influence.
"Hey There" is normally played as a ballad. This time, the melody goes at medium balled tempo, but the band is playing an energetic funk groove. This lends itself to a higher energy improvisation.
This is a relatively easy song to improvise on. But there are some complications. One of the most basic things the soloist must do is know the song form !!!
This seems like a simple song form, but it isn't. I would call it A-A'-A-B with a tag. The first A section is simple, predictable chords I-iv-ii-V7 and so on like a million doo-wop songs. That is in Eb concert. The next 8 bars (A') are basically the same, but now up a major third into G major concert. No problem if you know your Eb and G scales. And the third group of 8 bars is back to Eb, just like the beginning. That is straightforward.
Things start to deviate from the common song forms in that B section starting at bar 25. Bars 25-28 can be thought of as an "interstitial" -- a little phrase that connects two different parts of the song. The final section really starts at at measure 29 (the lyrics are "Or are you not seeing things too clear? Are you too much in love to hear? Is it all going in one ear and out the other?") The music is different in that final section and so are the lyrics. Before that, the singer is trying to give advice to the would-be lover. At bar 29, the singer is giving up hope that his advice will be heeded and basically washes his hands of the matter. You can incorporate these emotions into your solos. Measures 1-28 are hopeful that the lover will listen. Measures 29 to the end are resignation, "C'est la vie".
Coltrane's Giant Steps is a "don't try this at home" tune. This is the "black belt" level in jazz improvisation.
What makes this song so difficult? The song has a brilliant architecture that makes it sound almost normal. When you look under the surface, it is anything but normal.
You can think of it as two separate tunes. the first part is measures 1-7. Aim for the "landing points" at the Ebmaj7 and Bmaj7 chords in measures 3 and 7 respectively.
The second part goes from measures 7 through 15. This is quite similar to the bridge in "Have You Met Miss Jones". We have a series of ii - V - I sequences. Just to make things a little more challenging, Coltrane raised each of these ii-V-I sequences by a major third, which may feel a bit awkward. The landing points (the I chords) are Ebmaj7, Gmaj7, Bmaj7 and Ebmaj7. Eb, G, B, Eb is an augmented chord. Four major-3rds in a row. Those are the giant steps Coltrane was talking about.
If you are new to this tune and finding it overwhelming, try improvising ONLY on the yellow "landing point" measures: 3, 7, 9 11, 13, and 15 -- and literally sit out the other measures and just count rests. Those landing points all happen to be Maj7 chords, which helps.
"Cherokee", the Indian Love Song, has been done many different ways. This is a modern techno funky swing with the melody running at half tempo. This is a good platform for lines that include triplets to match that drum beat. There is a free-form section at the end to stretch out.