This is an issue that shouldn't be taken too seriously, but it will have scholastic merit one day. That said, I believe that the entire system of "Types" is wrong. It needs to stop. The word "type" implies that we are trying to figure out a mold into which we fit Phish jams. What we should be trying to do is identify certain characteristics of jams that are repeated or have had continuous growth throughout their history.

I suggest that we change the measuring stick to "Phases." In this system, there are four phases of jamming. Phase I is relative to the standard Type I. Like @Icculus suggests, Sample In A Jar is always Phase I. It remains tightly wound inside the chord progression and rarely ventures outside of it.

Phase II can become clear to the listener in the event of confusion. This jamming phase is largely represented by discomfort in the harmonic content. Trey might attempt to create change by utilizing a chord outside of the main progression, but still in the key. For example, in minor songs (Stash, for example), he might emphasize the lowered sixth chord while Mike wanders around his fretboard and Fish sticks with Mike. The distinguishing characteristic of a jam in Phase II is that at least ONE member of the band is still holding on to the original song structure. This is what causes confusion in the listener. Phase II is a transitional phase, but these phases can last a long time. I have seen Tweezers that exist completely in Phase II. However, sometimes that last member drops out of the texture and then is created...

Phase III. Phase III is generally analogous to what is referred to as "Type II". The jam that reaches Phase III is what many of us look for in a Phish show. Most jams that leave our jaws on the floor have reached the third Phase. Recently, Blossom's "Sneakin' Sally," Super Ball's "Simple," and the Pine Knob "DWD," have accessed blistering Phase III goodness. While only one of them actually left the original key (which almost always occurs in Phase III), each of them exhibit musical properties that are unrelated to the original material. This phase of improvisation is marked by changes in key center (Phish often does this with extreme subtlety and mastery), mood, meter, and general aesthetic presence. When Mike drops one of those fat bombs on the audience, you can safely assume that you are somewhere around the third phase. Lately, Phish has shown great ability to access the third phase, but has been utilizing it to leap into another song. What many jaded fans often wane for cannot be characterized in the "Type 2" principle. They seek...

Phase IV. Phase IV represents the great happenings of Phish improvisational history. 7.10.99 Chalkdust, 8.17.97 Bathtub, or 7.29.03 Crosseyed. There are dozens more, but you get the drift. Phase IV represents not only a complete separation from the original song that began the improvisation, but also an entirely unique moment that blossoms out of Phase III ideas. In order for the jam to reach the fourth phase, it must settle into an entirely new melodic and harmonic pattern that possesses a beginning, middle, and end. These jams are extremely sophisticated and require every member to be moving through the improvisation at the same rate. While rare, they are the very reason that many of us have been hooked on Phish -- chasing around the fourth phase.

(I can explain all of these phases in terms of formal analysis if anyone needs further clarification.)