Delta City Blues - effects
I think you may enjoy this article: Michael Brecker's Tenor Sax Into On 'Delta City Blues' by Miles Osland
along with Osland's transcription of the intro to Delta City Blues
According to the article, Brecker uses two approaches, quarter town fingerings between notes and lipping down then bending up to pitch. Osland quotes Brecker in the article: "The intro is an effect of playing a half-step lower than the desired pitch, plus lipping down a quarter step, emulating a slide guitar."
The way I interpret the article, Brecker starts his first bend of Delta City Blues by fingering a C# lipped down a quarter step, bends it up to C#, and then bends the C# to D by carefully opening the palm D key at the appropriate speed to simulate a slide guitar.
I've started with a simpler approach and play it at about half tempo, if that. I like to listen to these bends on the CD just before I play them.
I start by fingering the palm D lipped down at least a quarter step and bring the sound up to pitch, then, I slur down to Bis Bb by very slowly and carefully closing the palm D key and Bis Bb fingerings at the same time, which gives a nice bend effect.
For the next bend, I finger F# and then very, very slowly open the F# key, leaving the G fingering only, and add a little vibrato.
As my skills develop, I'll work on a more complex version, more like Brecker would have used.
You may also be interested in checking out Carl Coan's Michael Brecker transcriptions. I bought his book, "The Michael Brecker Collection" of 14 transcriptions. It's a very good book which includes a 7 page transcription of "Delta City Blues", a notation guide, suggested alternative fingerings, suggested altissimo fingerings, and suggested multiphonics.