Overtone exercises for the saxophone can help greatly in a saxophonists tone production and overall sound.

The basic idea is to develop the ability to generate a good sound while producing each tone of the overtone series.  The overtone series is a series of notes, or tonalities, which are based on the one fundamental note.  This is accomplished by learning to produce the different pitches that are made by using the same fingering but getting different notes to sound.  You do this by learning how to control your throat and larynx to make the different pitches.
For example, you start by playing the lowest note on the saxophone, whether it is tenor, alto, soprano or baritone saxophone.  Your lowest note is low Bb without the octave key depressed.  Play that note until you can hold it for at least 12 to 16 counts at a metronome marking of say 80.

Then play the same fingering, but you then produce the tone that is an octave higher than the previous note.  So, you are now sounding the middle Bb although
you are NOT using the octave key.  You are playing the first of the overtone series.

Next, play the same fingering for low Bb but you are now going to make the sound of middle F, yet still using no octave key.  The F is the second of the harmonic series or overtone series.

The third is the second octave or high Bb.  Again, you would play the low Bb, or the lowest note on the sax, but now you would make the sound of the Bb two octaves above the low Bb.

If you continued to do this overtone series over a few weeks and months, your sound will improve greatly over the entire range of the saxophone instrument.